Time Series Analysis With Statsmodels From Theory To Application

Leo Migdal
-
time series analysis with statsmodels from theory to application

Time series analysis is a crucial statistical technique used to observe data points gathered or sequenced over time. In this section, we’ll explore the foundational concepts of time series analysis, emphasizing its importance and basic methodologies. Understanding these components helps in the effective application of time series analysis in various practical scenarios, enhancing the predictive capabilities of models. These techniques are foundational for anyone looking to delve into more complex time series applications using tools like Statsmodels, which we will explore in subsequent sections. This understanding not only aids in academic pursuits but also enhances practical time series analysis in industries like finance, meteorology, and retail where time-dependent data is crucial. By mastering these basics, you can better utilize Statsmodels usage for effective analysis and forecasting, which is essential for making informed decisions based on historical data trends.

Statsmodels is a powerful Python library designed for statistical modeling and econometrics, particularly useful in time series analysis. This section delves into how Statsmodels can be leveraged for practical time series analysis, highlighting its compatibility and features that facilitate effective data interpretation. StatsModels is a comprehensive Python library for statistical modeling, offering robust tools for time series analysis. Time Series Analysis module provides a wide range of models, from basic autoregressive processes to advanced state-space frameworks, enabling rigorous analysis of temporal data patterns. The library emphasizes statistical rigor with integrated hypothesis testing and diagnostics. It performs the Augmented Dickey-Fuller (ADF) test on your time series data to check if it is stationary.

Specifically: 1. The function adfuller(data['value']) tests for the presence of a unit root, which would indicate non-stationarity (i.e., the mean and variance change over time). 2. The output includes an ADF test statistic and a p-value. It applies first-order differencing to the time series, which means it subtracts each value from its previous value to remove trends and stabilize the mean.

Then, it runs the Augmented Dickey-Fuller (ADF) test again on the differenced data to check if the series has become stationary (i.e., its statistical properties no longer depend on time). This is the landing page for a tutorial on time series analysis, based on Chapter 12 of Think Stats, third edition. Time series analysis provides essential tools for modeling and predicting time-dependent data, especially data exhibiting seasonal patterns or serial correlation. This tutorial covers tools in the StatsModels library including seasonal decomposition and ARIMA. We’ll develop the ARIMA model bottom-up, implementing it one piece at a time, and then using StatsModels. As examples, we’ll look at weather data and electricity generation from renewable sources in the United States since 2004 – but the methods we’ll cover apply to many kinds of real-world time series data.

Slides for the PyData Global 2024 tutorial are here For each part of the tutorial, there are two notebook: the first contains blank cells for code-along activities and exercises; the second has all of the code and solutions to the exercises. Part 1: Introduction and Seasonal Decomposition statsmodels.tsa contains model classes and functions that are useful for time series analysis. Basic models include univariate autoregressive models (AR), vector autoregressive models (VAR) and univariate autoregressive moving average models (ARMA). Non-linear models include Markov switching dynamic regression and autoregression.

It also includes descriptive statistics for time series, for example autocorrelation, partial autocorrelation function and periodogram, as well as the corresponding theoretical properties of ARMA or related processes. It also includes methods to work with autoregressive and moving average lag-polynomials. Additionally, related statistical tests and some useful helper functions are available. Estimation is either done by exact or conditional Maximum Likelihood or conditional least-squares, either using Kalman Filter or direct filters. Currently, functions and classes have to be imported from the corresponding module, but the main classes will be made available in the statsmodels.tsa namespace. The module structure is within statsmodels.tsa is

stattools : empirical properties and tests, acf, pacf, granger-causality, adf unit root test, kpss test, bds test, ljung-box test and others. ar_model : univariate autoregressive process, estimation with conditional and exact maximum likelihood and conditional least-squares Understand basic time-series models and the math behind them Time Series analysis has a wide range of applications. While it seems quite easy to just directly apply some of the popular time series analysis frameworks like the ARIMA model, or even the Facebook Prophet model, it is always important to know what... In this post, we are going to focus on the time series analysis with the statsmodels library, and get to know more about the underlying math and concepts behind it.

Without further ado, let’s dive in! In this post, we are going to use the dataset of liquor store retail sales data across the US ranging from 1992 to 2021, which is originally from Kaggle. One of the reasons that I am choosing this dataset is that it covers the Covid time period, which is interesting to see if there are significant impacts on retail sales. Before diving into the relevant functions to describe time series in statsmodels, let’s plot out the data first. When reading in the time series data, it is generally a good idea to set _parse_dates=True and set the DateTime column as the index column,_ as this is the default assumption about the underlying... Here we could see a clear pattern on yearly basis in this time-series data.

Generally, we are seeing the liquor sales peaking at the year-end, which is expected since Christmas and New Year is generally the time when people are having gatherings, thus the demands on Liquor go... Another interesting observation is for the year 2020, the liquor sales start to go up in the first half of the year, which is much earlier than in previous years. This is a bit surprising to me since I thought the sales performance would get hit by the Covid, but it is the other way around. Time series analysis is a statistical technique that deals with time series data, or data that is indexed in time order. It is often used for analyzing historical data to understand patterns over time and to forecast future trends. A commonly used Python package for time series analysis is statsmodels.

In this article, we will explore the basics of time series analysis and how to perform it using statsmodels. Time series data is a sequence of data points collected over a successive intervals of time. Some examples include daily stock prices, monthly rainfall data, and yearly profit in a business. First, you will need to install the statsmodels library. You can do this using pip: Once installed, let's start by loading some example data and walking through the different components of a time series analysis.

You can use any time series data, but for demonstration purposes, let's use a dataset provided by the statsmodels.api: g��ɧ[4��N�[��@��Fw��S|Uث�Wb��]��v*�Uث�U���_�b35G�łӿ��Ayk��i����y�\�i]�T�v*�Uث�T�S�kO4葕�z�]Z� :"�(ۡ+ ���Q�u���^]ѯ�����H��s�*��֛Uث�Wb��]��HuO�Lt������}��v*�Uث�T���o�������Y��0]�Qh1T�I|�`����"��]Vv�7�S�)��� '�e����ꒈ��m,���s�h���a���m㶶��!H�E�l��a����]��v*�Uث�Wb��]��K���{o���*�b��]��v*�:{b�M:')���D�� � � BG�G ��zК���/v*�Uث�Wb��R ����^�q��me �O<�*��.�n\*���]��v*�U*���=ݑ'�i­ =1$�M�튬�U��4v�䦗�:p���H�3Ъ+�^تq��v*�Uث�Wb��]��v*�UJ��Ћ����p8D��~��ChqM�n�!�@��mJ��44��*��]��v*�Uث�Wb��]��v*�Uث�Wb��]��v*�U%�a�3i���P-n��S�&9��O���_兞M=� �ɩH�hUx��� }�U�=늦���Wb��]��v*�Uث�Wb��]��v*�Uث�Wb��]��v*�Uث�Wb��]��v*�Uث�Wb���mWT���M�6�Gr>�2ӗդF�`��с�b���U 6P�*�Uث�Wb��]��v*�Uث�Wb��]��v*�Uث�Wb�o����-�����[S����u�F=J%G��{{y7�e�G��9o�v�b��*�Uث�Wb��]��I�ץצ���������X^Nr�$���Zw���O�������9$��ITgPYw��LU�1�m��#?�V�V���:��w�=�ޠ���R�U<��:��M1Wb��]��v*�U�$)#r��R�E�,ְ�%մRH�����XT��v�U~��/�m���g��ت �5[�i�E-���L�\J-��H�� sI���]�qTo����-�����[w����-�����[L�Wb��]��v*�Uث�Wb��]��v*�Uث�Wb��]��v*�Uث�Wb��]��v*�Uث�Wb��]���� endstream endobj 306 0 obj << /Length 2521 /ColorSpace [/ICCBased 59 0 R] /Intent /Perceptual /Height 166 /Subtype... elax .1.1) /F 4 /Type /Annot /Border [0 0 0] /AP << /N 605 0 R >> /Rect [218.28 358.23 222.514 363.946] >> endobj 311 0 obj << /StructParent 149 /Subtype /Link /Dest (figure.28. elax .1.7) /F 4 /Type /Annot /Border [0 0 0] /AP << /N 606 0 R >> /Rect [333.12 198.53 338.101 205.355] >> endobj 312 0 obj << /StructParent 150 /Subtype /Link /Dest (Hfootnote.29. elax .6) /F 4 /Type /Annot /Border [0 0 0] /AP << /N 607 0 R >> /Rect [301.44 174.63 305.724 183.357] >> endobj 313 0 obj << /StructParent 160 /Subtype /Link /Dest (Hfootnote.29. elax .7) /F 4 /Type /Annot /Border [0 0 0] /AP << /N 608 0 R >> /Rect [87.6 138.63 91.884 147.357] >> endobj 314 0 obj << /A << /S /URI /URI (https://forecasters.org/blog/2018/01/19/m4-competition/)...

���G+`Ywh��ڥC~����y�J�~�PiOr1��/6l�P�������q��m-Č*5b@�`-[�u�v�J�%�'���к5;�"������a��+)�1�n8�h��R����W���!�� �Ҝ��J�,� .Ahш��M>����=0�]�G��k�k}^�b���L2K�f%�(ff�È�"�Nj����`Fƣ�ئlٲ�Lo���9��G!�an��Yh-֯ql�mf�GHQy�P��p�#h�(w*m�@�� D����|_����� ��Z?�����Oi��G5�\�D0�|��V(dD�A*N��yy��lٱ�I �$��n�I���1��f½w[Ѵk%�ե[<�~��-#T��q��;��/��B��=�[Y��J��o �wR*0vlٳc �����H�?F5��#�(A�(@���0�<�'�!�:[L��e�UA(�%�ET?k��0��� ��YV���]���Eh�;���3��m��"⺏��?����2�e`mJ���O���*,���pXrs���g�����1���1j6��[O�i�LlL�Y�����f���>ȮO3 ��Y��y�Yh�rx�b����o���WXDv��E�x�+���jW|�5����Z^[ηQM��^�i�����r�ee6s͋�*����������u_�\���lK"uF�F�4>#l(�.<�r��g��u k�M)n���d8z^�Y��E��"w�gem��S~�`�/6l�~a�<NԜZ�n&���d3���*�X�iV�9 �V�k�~�����}����ˢP���,1 >��Ϋ�e��ƞ��l�tk�|Ǫ�F�k{�t6��[\]\K�e��]^��5Rh��^�"g�a�s�.��+-^�� �0��ef���J��h�t��8 ��G�r��;�Q憷�n#�"]<�NY��2#�d�>�%@�V�5� ɿ-5�5_*�=�����Euj�oI� P(�a)O�J�f͔zd7��0j:���˙&[[�BD�H%�궓5�djPz�:�D�yR+�qs,������Y$�d��Ȋ��bUJ���{�:'�t�}SZ�t�-�����H&�ʶr���25z��]r�C���n��U����˻�Y�nc�$X��J���)Q�J?,G�J�i�c��-vӬ��ޛ��w5����Ή���x�'��/^�"v����%S���8���;+� ��Q��\�8�Q�v�F������Wq��ֆ��)A���;/6Q̀�T��͗I�������q��S�R7����u����ձ�P���S�I����>��_����θ.���VO?-J�sM2�*@0[�#"�~���tJ��6l��!�w�� ng�b����8���ʇ�=�s�¬��_��Lڮ�f�Ҷ�6ӣ��9����9�z��M �t\ٳfȧ�|�G�=]��H�1���̎9J��e� �2>���jOgqv�G�t�-<=��*[�zmq�$ �6�R;�^4 � nf&8}���*�\��ۍ���ئ��ʗ�7>X:���(�i���]"G,��e0�����z��#���*�����?���G\p�͕��<6�I<�����`nk\'�|���r孴�%���.=9���cn!��H� �a�a��+(��9<�����IpWRVD`a��" 3?H;)^U8v�v;6l���*3 ��Mr��x���Z w���@~ ���R�$eY�J��2������?���G\p�͕�uK�k:���6���9���J�+E��+��:����/[Z��ŽmBj�c?%������p�O�]�{�e���=Fq6j�G���L^d���@���Ȏ�P����F�_}��N��t[�mCK�����1M���r4���^�;6l�M�9g�%�W>a�nϯ��+��\��'�Dw+rx��gXZn*�Uzz��W8�y��Fc����m-�W�L+Z���=3�~b^[/�� Na�����tv�P��<�r�V�̡iN��j7垱6��[f�f� $w������� �T�����flٲ�L�~m���"m^��&{���2�s���0n1�&�zS ������h��yhi��V�}��Rݙ���Db�V_�g������[,|�����(�V����X�G�ןZa�a���{���{h�k���zs�)(��l�:V�ie��Z_&�.��$o����na C��gq]�V��w4... }U��h����:�l��=��4�Y})�-��� s)QC�Z��3/6Q͜�Ϛ-�Ǚ��n�P�H6&��i�%���/�L�v(��~Z���K� g�8Ӵ���zW7֭2���`L�#O���?�m���4v�J����+���m�ȶ���M��Eخ�-�y��T��'��iuoZY#14*�S�$���e�֞9�3f�?:���Y�]./^�� ������e.R�j:�K�p�Y���Oԣ���40��$�t���ϯ��Q �����|�9�^l��� �@IS@7'l�z_��zV��h�%���a 4?^����q����?�4�F�M�E����<�����4�tr ��-|F@���s%�X�yz���7���������$2���5U-χ* ��~R6��WV�I���2�Gy�y#��J�K͛9���u |ĭqeysb���L�z�.�ՙ.�ELnGBxһV�~^�Q<���o5��o$��J���4���0����$�y�����EMWV��s��z����2s��(2�9�7ȟ�|�u-޵a�=α���.����-!X�����?�6�$�����4���Mir��,�V��Q��fV�t��27$���o��d$�{��b��vC#����B�#נ�~U��yJ��eYj>s9�f�9��ͷ�m�sm�o�x���6�9��ͷ�m�sm�o�x���6�9��ͷ�m�m�l�f��6�9��ͷ�m�m�o�x���6�9��Ͷm�m�l�x���6�9�ͷ�m�sm�o�x���6�9�Ͷm�m�o�x���6ٶ�ͷ�m�sm�o�x���6�9��ͷ�m�sm�o�f��6�9��ͷ�m�sm�o�f�6��p1�2��� ��^/��Oc�_���_�����#��{���E��o�ߴ?ޯ�rA������#�Ǘ�����������o�B��HY�� 7�!f��,������o�B��HY�� 7�!f��,������o�B��HY�� 7�!f��,������o�B��HY�� 7�!f��,������o�B�?�c��HY�� 7�!f��,������o�B��HY�� 7�!f��,����������o�B��HY�� 7�!f��,������o�B��HY�� 7�!f��,������o�B��HY�� 7�!f��,������o�B��HY�� 1��M�����[��p��?폱���|�� endstream endobj 334 0 obj << /Length 27843 /ColorSpace [/ICCBased 172 0 R]... E��k���S@�6(�����u�3Q������,c9.���-��h���'ٳdW�uѭ���k����VD�.��_��[�� +����_˱�Z���\Z�&�,G��qo,<�s#ܣ|1�ު����:&]sW(�ͅ����j��k�Z}�-�m^64�E�����e��]�w�^m7��ŧ� �hy��sk��� c<���SK����U���!��`g�j�Nr<�|��i3��.���>�/��=�n�����)n�&�+'�.�a�yF; ;j�e��hE#J�����S�96��'[K|�;鑾����{Y�Iw��Ew �%�2�n>�p�N�y��4��m!������"�4��@����N�3���߳������������Ď%�6lٰ&�� ?O���-Ϣ��/)\�T ��h>j�+}u�\i�ZV�i7kvbf0��0������p�6lٲ�F��=����� ;�COqim|���i�w�+4��z���lٳf�=0�t�|4�{o����֏�����\���:e��^��}B����!f�������?����z�R��W�Q�S������!Y�6�=2��k�ح���\]�go}o=�����7�(hyƬYh|F ͛ <���;8��k�n."������I,��22 �����k��Qj6���!dx��I��J���mU$x0͛6li�'�t�k��n/mຘ� ��F�9cA��5Nƒo��Wr�[�[�{~�kѼ��4<�V.�&����gF��!��-m&�V8�'�'a��We'��[�^^��Y5[$k��5� ǿ��Ŷ���9#�H�lٳe6W��^Ц-N�Af ]����* ��x ��S%��IqK,~�Q��g��z��ԥM9 ��C����i�SZ�_Y_=����֙V4u�F�^���l7���-M��aI"����9J�w�ZV���/6y�]�D�M��KtL�A�}I%�A*�*���/˚�����"�ܤ�ż�y�,i�djW��i�6lٳ`]KT��-���aonα��MK�27D]�f���E$rēD�$2�x�BNᕆ��͛)�db�Ϻ}���F���ӎxm$ԇ�m���bH����$���J A��6l�D栦\y�DD&���Q�%�) ���.���& "��:�����]+N ڍ����!�h� G^&B�ď�����V�Yz�6��0��.t/^K�-/�{{�"u� ~�~�ʃ�Č�eTr��8ֹ�y���?OJ�>d��X��F�5��!��J�DPҼ�RE)�,�Ť3�e����:�*>˭Mwųf͔��?��]R+��ׯ��{i"��ݠ[wvB�x��T��l�ySA�ɢ�Q���qyg��ͤ�v�S���H��$m9b��� �놟�>_�tK۫mb�W�Kh���x�E �Sj45a�Ӗj�-������.�J�����օR�(BGI�� qN 8ӾN|�ewg�� ջ�����N(xKw#�|�X���·�g����[�1u�l�@72[WF�ըƄt �?����c�߭֟}�<C�Ms���9o��b�+z����t<ٳf̈́���{{�%�:�a�Sejm�,@�GԆG��, t�GG�nT�}�ob�����kʻ;� *E�����lg�|���yws2B�ǘ�-yX 542fu�<��S� ��͔iQ^��<ѣy���\����5���-/P�5m5�猢�pQ��%m�r�6Χ���i6�<Z����\�... �~��|ٳf������_�w�u�K5�Ǥ7eU!eVj�ۢ�O���3^j����ơ��P����N�#��Z9$�Ӡ� 13�l�Xi:��ꖫb. 2)U0\��|d�j*��]ϕ5yn��-�R��qj1�*- IOJ~��S��o����K�.��:�j���"&�ԊɤfA"����:l��A;� ��ג��x�����'�@�a��\.,�*��[w%��Z��Nu+9f��'�6�:)�ز����9'����lٳd/�~Q�5-f��K��/cۻE�ȓ$�k���>>p��,�n����H ��I,�5�-��T/٣! ״�4K�y���FK�/0�m z��B��#����.KL=�n�}�C��v%�2[��y� �0�}��gc�,ٲ7�3X��-�� ވ.RK�-���:4^����F�҇ <��y�J��.���L��(,cy�K8���@���x��M�d�,f�r�a>��m7Q�#����'�x�[�\A)M�� �#�D�A���>�^^�H�~�����*ֲ7����ǹ��וD�^j3�zڎ�y�$�[+ɸD�C�_����NH3f�:�*��|�}>�o����IV��X�*Z\!I-e���*��>�W]�����V����\$H�[Y8~�|'�v���f͑ȴ{��]OTx�,�4�l��C)Qe��q�@q���|��d��ť�����"������F��j�����O�4O2M��u�i�Mwom���!6�r3<76S�W Z����c��yCY��C���.6wzԷ��5#�2��n|�Gn�}�&�H�N���F"���X�#V���@˱�����߳������������Ď%�6lٰ�̚�����j�*^88��R�H�#NLUW��&��Ư��v�O|�z� E�6��QR�� ��W�f͛(��n��۹��.�wc �����+�1���@Yn"uD�9kD<�OL��͛6l#8�mu��o��픽źC;�Q��:�O��߶����_���L������5�q?��2DX{�p-���g�\i�:�����ѝ���9,e �`B�S�b�y���i����/ku��1C<�j�F�*�;J(vÛ[�k�h���Ym�P�Ȼ�+� <ۯ]�dW6��\�5�6�\Ha�1+q2K*��D�M1O+�������[]V��7.,̵�zo� (����f̀��[N�4��Jaoel9M1 �A �3�a��~����j�n9,�Ο�qr�������|έ�];�Z���f��kɑ@��דn�q��|���ͨ��#��܉�*��Fb�UԒG|1�����f�{m2�n'��@�'�M)uP��j0�6l���/�3iw0Ŧ�tm>�gar���Bʨ�U����m��ٳf�K�7�vs��g��!�X�r��eFAP��l�#��_ծ�����5�a� �ب4%}x��N�k����ʚ~�&�y~"���/Jf �y�.��V���>v��ȵ!z^�g1���<��_� �0�ީ��놖�z��W�r�����T}GpEG|� <խ��3�[[���XbD��QZE����9rcLOʞbmoOig�-�br�A��@;K`��?�Q]��,f�r�e�b*��L��q�6F�� �����hP���~ԥ�ʽ���jz~�j�V qS�C��+���H�*���f��m��o,��.�%�_�a�d�32��h��q ^�u��}�� U�*C)�05x���6l����<��׮F���3A��'V���--.#�n�R��I�&E�6�#FpO�i�yWZ���%�(�__i����LŶ؀>�j~F�����E�_�� �c����]ẎYE�dq*�Hz��%�S�L��M8i!^Gkpo8��Y��;�ry8͑�<�:���Z~�H�d��I�4ٟҊ�!�D�~�+�TiB0��\����]]�$m�1�mn.Rw��ݙ��Tʬeb��'Y�W5sf�mO�:����y�u�F�����8�D?v!���g:�^^�ȡ������*ֲ��Ff ���_w����wu�\\�V�{�UV'�,p�S�F~ON�p�6l��9o�<����u�Xm�]BY��f�$�[\!Im��`��+؍��t}�K�[�u��H�%�I���B�ZW� ͛6Q�z��6>c�����(���aq �-���2I(�]����i���K���WP�5Hu+-4�j�Cm�ÊUhǦ�4�6���M��V���Ņ�����"��6��xJ�㌵#y��_�'op�$5�Y̧y��;vf_�%��y~���?�;��^]��w�O��ijf͛6Ԏ�,�:j��ž��XI���`�O��.���7~k���+M;�������O�i8M1`���W��d�6lٲ�!~�4O�������s5��H�� �*�F��O�jOL�f͛6Q�y�A�j�[�O���a���Z?UJ�*�C��\OI󆁫jwn�,�]ZW���,J@RW�d򣏇�p�����]�4�v��KmB+{��OB8������Ƨ�v�ۧ�It P�V���w��$ ���C�<�����̈́>r�o�].;�(a�Y.a���g�����L�... ����Kj���)m�`�\"�_�;��/�R����� ˋ^Q#ƣ�~4"BIa݆Ƕf͑�:뚆��%݊��=�0�qw����G�_L�qA�\S�a}kJYnV8u(�.��&�6���eIW�N[�sf͔z`{��-:�{�ٖ���K�3�*���;|�?槕��W��Q�h�0�X\E+��=(�h���9��wy�]2�@����Ȥo�� ��2�DC��`8ҸN���YE��Vs,�����\#@�$��%UIT�8a�y�A�.���S4Q�ǭ IJB��� #$�2퇹�� �y�T��mΟy�ZM���@}E���F�/efoHC���퓰A����͛�XI/��d��uR�mN(�Y�id�4ufR�⼸+�l�W���KR��^Yޔ2E����E_�b�@�ǽ0>����3U�L�7_X������B�2� �8󓢯s�e��䲎�w3�$� �e{������Qxs^UTx�֕����X��[�P YYOGS��0�)�p^l#�}��R���ΒB��9#I%T�Yxn�,h{b^M�,�Ճ � z�F��$Gq�.#���/�ٳf͛j���u��KIo�6_^+a�e���H��!_�]�7H�4�bݧ��ap���� ���d?8͛��|����m�N� Q�[�~����fݢ-�"ސ��"Gl�#�����dq� ��f͛(u8Z�c�#��t�f1^�ڭ��E*��3/5s�P�jL-��0����Qi�p��ya���eX��h�X̲�2���� u<��� ^�T7R�pY�\B-�t���,�,��UHU�g��^�V��Ḃ�XV�$_��̥��Y9�dڞ�k7L.ӿ�g��������q�d��K6lٳa7�tk�cC���U��I �*cg��e�M�9N-�p����Y������ieu��)%����V_�.�2I·��(�6lٳc[�rˏ�_65�v��;����}IR��!*̰]��xԳ;�s�DӼH� �;eH�d z�b"� �ٳcO\��yѼ�ei���*+[�r�=�R��s���\, I��E� �&h�zU�عd&���b Z�r��z����C��G��R��N������%�񤕮�Ў!��2߻��y'�u��]�ܺ;Oww����$����s�6F<�jڙ����L����m:��� ��w�~D򶻠��R]�W�z��E�d�ژWӎ�.h��T;B:S&y�f�=0��Z#k�[��Q��%#�VGY�����EƏ� k���m��'��M�2[<�ۺ[_��(y#O�Pl�6�~�u��~������Y�t��CYʮ�'�6]�i���>j�Q��R��H�[��֒����AP��"3"�Q��|1��-*�J���K -&abL�ȎYj�D��6UhA�N�˵O�_4]����c�y�乷֋ʷ�)J���B��T)����-��bk����ㅋƯO�#0V+^��[6l�����~^�S[�6���{[x4����G*�}���R)\��O��^Ӽӥj�vZU�X����RM-���"��F�|L9�ڷ��[˽nh��.�{�\ۆ-P� �P��j|4��[����T�S6�~��wq�|�$ �p�&�5fYP�� z���a�4Xlͅ��Q��+w�R�Z��*1�Z���k�#�tе=Z�ɴ�!z}�wimu�[Nc�C0�<��~,,�g�<������ h�:�h�� ��Y��8���򍌬MiN�rm�6lٰ�R��MA5GK���5�2\(� ��^�F��/)ZZiWW�/�rP����Q$H��I����-t˙��K�^�B���~"+Ȥh6�>[����͔M9̵�˟2_b�lͦ�p��˼��[���Xx*2H�IM�|;gC�R�4�X��(��RT�fx��������͛(uȇ�|�u�),�����tY���ɞ��eC��Ʃ�N�͆��߹��ړZD���m�1�q@OJa&��yɵ�^�F]9�u�(,�[�%Ya��^n��n�U�`Xa��<�q���P<�=��h�n*ӵ��ܙ@ţ���n�_��~��3/�Û�����2��8�lٳf�o6�S�����Hm�#Y.eXVI)�_� �F�ε�˫�:�%���V�I{`!�+�"�zl�d0��[�d�6lٱ� 6^|Փ�WVZ���J��XdEGI���m<җtu��"����@͛6li�XC�t�|�{�[���^i��Xm�@����}NC�u�E:헢��K��4����8�ao}��4f@�ҿ<...

J���֍ƣ~�k�2�f�̈́:�����ji��[�%�S��ss�"��qȉ� ���W��[ٵ�>���;pW����iL\���«�*��j��3�6:|D<U����\.�q��"l��k�UP�tP� ��f͐�� n[�P��mb����6 �+�"U�ȍ�q? 5 z�y?H���g�D���nmN���L`il���2�X��R��V�΢;,f͔sdϾV��5xg��R�Ź�5y�0�:ʷF�~�.�k�iv�~�/E���>�gok8 �ҳ���������b/4�%}o0E�H�ֲ�n"�8�ޤ�ZP�~����y���Z��Hm�o�����;���X������z��sYy[� �yn7ә&��M����+��N�)��%]N�9ӛ�2���[O�ʿ����w�O���+�3f�9�)�~e�kJ������_�W�V�r�mܓ$�8/U;d� ��批G*�FՅA��y�eed_I���Ϋ����k����C<�� ��B�8fo�F ��rN:� �َVU젓��S#�c��#}�y_�#]�������V s�md�����Ӷ� �4�������9]:�͛ ���/��[�~������o�/q3�Ľ8���C��ޝ�i������*ऑ���wGZ�q� ���e��7�x�x��1G�H$�Vo� � ��T���3qjr�i�M�f͔�����������1Γ��֥�x��2ė ��z��$���,e�͕�62Yb�'�WX�K�#������N��42�4� � �D�ʆ��ª��b;�͛6l)����/ح���4RM�Q[�����HEH��bi�/@���X�sOg�RXfC�8��bo��ѻa����eي�+��Ɔ�F7�H$�Vm�}��zNJ�]�_�ˉ��CLct�X��-i�W�૿����2��8�ec��l�G6B�ۨ���]�f�� ���=r��E���H%�B�H��1B**d���젷���i0 �"���,�e�͕�uK�g��݈̦�&/W�Է�3�j�W�m��c4SB�?�ksʹ��� ��$��~ߩϕ�?whYZ$eq QH ��m��y���~h�Gyo���$����pN!��f�؆^HU��9 ��"�,5�F���]yoV����y�q��tuf+%M��N ��d����z�]U�)s��M��4��>}Byn�;�/��\Ӯ��`!��7P�"�����M�����2��'�Iqxm|â�}�/֮9=ż14r�9% Ͳ�|����W~E�g������[���Hֿ�Td�6l��������$˧]H�wg��X�Ex�F������)^�����Nu���/�-�����xT�G=�<�qs ��tp�J��t����e����ZN�u9��Pk��t�����n&��(˪FR�;R�n��O����i�T���� �-�����{K�ȉ��yaF�����&���e���o(i7rL,�.���8%��,�u�D��2��"�=�Y.���up�����d����Q�V#1J�@9ӗ�!��ͺ�V�c��� ՞༺�׷�s�f(��G�3D8����n���N�/6';��I)˂3q��4�i�'Q�e���o�d��Mw<DG��:��4Wd����YU�(��:�k���I���Q4���H8л -�v�pp�2�f�̈́Z��z��& )����ܗ q�z,jS��V��x}A�X��WI �V�N�N�����>� G� q�����s��5�w�LIC+;�}h��P[4�3��.#�9Pr�J��^lٲ��x��@�Y��K�Ś�Uz��{v_L�5C!/�M7�O��B����Z�������... ���g�g@�>�~?�M+����~|��헔�(��M)�K��k�&��1;\F��||A��d���-��g��zc2]�w��zLXzW2s@j�Q�ˎ͛"^n���>��k����� ��b��z��"��d A����W�(y�C�%��46ii���ͤW:٬%�8�F������ �:闖3f�9����3Y��5K�?C�u�mR�z��zSB�3����#rv�����Ϛ{��4�M>�N���d)~Uh�N1BC*�ف��&6���d���ui�^)�(�r��t'�Ȟ��_<���wL�#���<�-�Y\Iq-���.K$QpS�hNJ|��_h�W���f��H%1�W��q$/f����66TE$d�#!a�rT}�ɯ?-��u��<�$zx��Y~��$�%����ı&E�O��s�yz=V-"� R`��5���F�2�� ܙPՔE6�<�/6l��_w����]�iv�7kN7A� t����E�h�/-�E��c� p��yQy�'bp���w:��y����%B$�NA�Y��w��C��A�4�Z|�� ��e�͛"�v���w�j�!�MCI���^1Kycr��8Y ��Z��%�ד�צy�o1ImcZ�F��M��W��.BNvՍjZE�(�rz�D\���6Q͑�@�쵟3�\�bb[w�11,�+H�O/ �������tX����{�efio�D2����`�/��o܍�g�-\2��k�]���$B��]�ѓ��H�H�Q#UD ��}�͗�6V�介N���?Z�!����yB����p-GY� ��6�.<�w�[j0��Ŝ�~R\["W�)É�N|��iz���i���u�]�́����+���`�2�f9Y�մ��O-�^F%��[�I"aP�\��y���V�ݿ�n�I�������������9J�m��e��ꧮ�N�}gȮ�p�0�y���/�� ����^����,��}ߒ4�ЛϦ�C Y/����C+�W��p��gQ����3[�_�ڧM���/qٳg>�̿��Uѭ5�Λ�ˆoWV_���� �hj�<�׷|(��ס>i��弉��� ]h[�7�ݤ3\�����ڛ����/,f͔r��p�1M�KO2j�5������}gF�D��mZ$���̂��%G\��Y����Q�_U4"��[~�9��7������Л�B�0@ ��rZs3�W��p�Nu/�Cѵ3��R���d�u�f͌���C� F1���S���`�����0��a���O���U�2��q#H��c ��T\̌�E��"r��z����:]�Թ�䭲\z��\Gh���X|\�#��t�(Հ��=�2�f͐?�B+o���Nm<�srR�|V��$٢�W�⚭6�����i���u��Vŭ4�B'+�rf�� �c,��U�s���챛6Q͜���^�?�<몽�W7�Sًi]��*x�Q��}wC��@�,�M>�W��-K�zu��SZ����ב�5�>.�:��u����;;�R��mnx$P��қb�FCd�t�K^���8n��5���\*�x`2� lV?�7�6��eݎ�<������i�g��d�ޟjڌQ4����͚���65���n*��M .j�в�?��X�QEP��� /�T�θ�4e�[xDt"��>|x��JV�3ִI��ԍ'�3��;�L��w8�^l���N��I4BZ��]9x!��>�,Q�o�IQKRueڇ��y�W5se\g�nF$/בU�~t�EUu np��U��5M?N��7��:X �wh�28�E��� �k;~Yc��p��eNn�A�&>|V�y�eR�;�Kƶ���K�'� �4���T���ZƊ(�x(~�٫����6lԮԭv�PP��`��͛6lB�{x ��� � .:����V�aq Mja��9a��{UYj>�\ �٫����� $���@��W��-�uN��+x�Eʲ��8��SJ�\2dR~%�ڠl�N:�hMH����|kAn�ĎǩdR~�3H�... ���[7�kݸ�Qk7�5��E��,�J��D�6�d��n�i�&�9�v���`����ZIs��W�˔_sx�ѼUC����%�c%nk�4����_ �Z^� �v�-�Q�E��WZiz�f�Ǧ��fۦ����\������r@����xN�jל���T��ۢ�e�44���L�ȕT�~: �ĕ<�]%��=�� �E�Yh_�0 EJd�hQ�T���u�U*����yYx�e8�� ���ڃ���%�ɬ�#ݜ$�b������N����H2��9s��.��}���&��!�|_��6%��j��Tt� h� � I���>#�t�rW���U� ��nO����a���"xY�腛�� k��o~�4ɇ�� #+�Б ��MYp˽� �s��VQE��e�� ͸!<���N�2*cu�%��aX��/�^J{��#@��F���Lc������K�|��d܏,�UjlR���]ۨ7���ᚚ�H�J��k0X���̟�}0�����@lxy�a�i}tP$��� k"�)�2��X��!�����^b��l���7��5��lt�oCO����sg� �C�އ��t-�'��N\&:����J��a��X.��ؘ ƴ�'�-�ʠ� ��QU�G%8�/�A�W�O�HS����TU���0�����+2B���0����)������A���{8p�7�VʒĒ����P�G��k7?8��S�/E endstream endobj 341 0 obj << /Length 66 /Filter /FlateDecode >> stream x�S�*B�.=Sw0�Υ�id�`���e�`�� F��zf... ݘ7b��=���Q��$g�FI ���%�a����@�W�n3�\Ӛ�_�l��L�� x�� Fߜ)b�L�\pl�ZQOǘz�a*�S ��,����(���T����#h�i���ԓ�W��\���hRTbDw-�Rה����+�G�‚�KX-f' �d �!���#%��8�qp�@/�Zq�dd�A���ݒ�Oq��g�"j�7��J�4�r��j�SH�VljS\kA%i1/�W-�҈]z�|�|�2e�ؕ�ef_)�� �"Y��#Z���z�#^����c�����as�=�jvӦu.[X* �E"�R)}-����U3� �޺�zA��5 B")���l����p��Hv�䈂 u���1�v�|3���e�p�&�*�2��Oc8sDNegU �\i�==[�v��d˕�J���[)�/�=���R � WMH�Z���{&��E��{����g���>�� endstream endobj 343 0 obj << /Length 29330 /ColorSpace [/ICCBased 172 0 R] /Height 243 /Subtype /Image /Filter /DCTDecode... ���:X��i����5�p�y{%��/,�g�''d J�>A��:����8���W�"����m{ �r�� cXQ���ҹ�r��Xy�dw�F_'j��ز�xZ(n e!ۧ��v�"��i��鱥�6ڜ�Ci�]J��m5�"i�g�ݸ�#Β^lٳf�����; C[x��I�]X"���(��D� k����nFy�[կ���5�K{}OM�4�٭䁣��!8�@~C�5�%~s���]�Z5����t���Ǒ#N��& [��N�M�~`y�k�ot�h4˛���u5�$����9�ԓ���S;<6͛,� O4�#H�wv�nI�1��Mt+��I'�qn�&��4����f��L�F�'-���;M|E�^l٫���#�/ȦY��z��3��?�N��ՏM}<ɥ��'jp�=���K�P�LY=DF��1�l�/���T���?Z J�!�� �[�,����NI3f͛9'��O�K���&Owk���ҭ���-�C4@���+QTe�rt�/k���e���$V�� bIh)�~%�o2͛6l�G� z�AѿJ[ۥ�p��W, [��4�ǼiV�|���}���6�a���i �M+2��\�F(O�L3s�J495�,Ck�[A�j�d�:���B�~=��~b��U����=����;���������L��r�t-�˳��.c��t�7�����;��=����e4�$����)֧&>Tח_�톰��e��HvB:��ٰF���A��ͨ����p>lٳf͔kCN���D4�)����w:�λip��Eosj�&2b��� ��qj�ji���e�͛6l�y�ʺ���i�Ώ�.��X���,F�mڤ���� ��`*�P�u��TjPLڱ�5xR��L (�|m����o]�2a�2�f͘u� �_�'�4۝H_k�jijK�Fl�\����n �ǂ����h^^��vk� Y� .1Gd�$�dR3s�}��\>��c�L�ٳa/���<��5�ܵ��n���&���PZr;Tdw��)|�g�[�n�Mn�}����[�VDx�V����v&���8��͛6Cu?

�}i�h?HϘ���_�'���*R��>\=���!˩y�}\_��i�Ʉ�*~���#�!��N�{᮷�����R"��^�)��� !�ʣ�=J�8U������߫z�녽/��)�Ч-�ӗ�����b��<�m�������:�[����Y7$�dƻ����6��6@���O � I��s���wQ��4�W_���M��ӟ�en#uj�y���/B(*2d��i�L��@�x��Gz|L�ո�{W��͛6l�|�� ��>�R�[Kk���G�xj'0P�X$zRJ= <7Ĵ/,��"Hl`�p>�|�k��]��K@dos���f� r}�y�3j�6�Qy{Ys%֙sjnY���R����_g���]yE�H��n�l�w`D~��줇�s`k�m�ñ��6l�Q������qX.�x&)"�a��G�f�����G��Q�9.59P�+��� W��?�����щ�@c� ���d���o�����r��[�b��[3�K��Kpes"'��h0�N�\�w�ɽ~�Ҥ��=:z�A�k�᧥�}�ᇔt����4V�Md���/|�g��>�:��闂4�����mC���s��f͛6lB�[��%��/^�������#"Vb󽞽�i�d��8k)pb���R&�@�I�1R/�ɘ�͛6l��u�$i��)i��B�����-�E����"�*R�N��e�th�bK{�&9�BB����jĸ���-釘��/6l��uDgo�����F��|��k��N�#���n�/��9��ۧ�LKK�u]b�G�� ����n"JL �A�2�ۖ7_�וt �k�^�. boM!�b#$�M�#�S��o&G|�O��p���M�,щc-' � w8c�y�A�r��u��q�Y$�������� �f�7k7:/�u-V�qsiI ,�0�-�,+�5=B��M����*b�����2����]�:����r��͛6l�<�Xkߠ>�N�Q����2z��Z���KN��򆣩��kz��NA#����z��ƈO�w��b�g����7_VK�1�H䔻�,@X����k?�GP� ��5%��,�'�*��͔'-��y{e��|����u���c���V�ৢ�����æ^Q njGp:�<����}��ǫ[��e���/��Vk_JWE7ff��?��Ԍ�9k�͛6lو t��wYM�o���k4p/%�r6�k3 ��T�q@[~����隭�]i� <2(p��=9�h�}��3f͛9����0��a�� [94�>kh^��o�X���nzTB)R)����X�H�d��Uу)�Tp�͛6l��5�!�����/m��s{��Z��&Ӓ��R�����y���-l(��n\kZm�n�O0��o8E6����4�����+El�(�@#(:d�J�����7�l����ؤ7%h�H�9uV�T0�JA�͑��X5���)�I���K�X�i�Py�.�ڢ������ZN���S��Ŕ�<�t��%���!n�B���G�X8М�k�͛6a�!�Z��m���;�j�=����i�UK@����P��=����[�-Ow���Mi5 [�fkƕt�YeF��w@�™���cys�)M������-�ʵH��L���� ��h:�����9#�|��=:�7���F��}�6vv�z�����{;�-�)g�H.���ȋ�S�SB~�;CT�'s]�Z�����W�iw���,7�B�i+l�+)����^�{��o�yT��$(�`70���(.D�Ū���kƋ�;]���ZEt�Kl�(qop����W��O�p@�͛6l���}� g����[��S���Z� ����v3yWK1h�������_]K:��iߛC۰S�6��]�u徻7�59"�Q��a`�(U������/"�2[�6l•霋U�ס�u_�i:�Ϙ���� v�#qj��n;N�� �,+�&?�p]�y7Nү,��������ʜGM̐�ی�٨2S�͛6l��jv2YM4�G-+-��o0���"Q�A`�|�_�/ ���R�3�.漣Ԭ+$���ߎGu-�����xt�����ơkq�yGq%�k,;;0 �y��;�!k�2�SA��ad��cx�b+���/�"Vqy�Q��&�N��O�Y�Z����[ߋhP�tCH҈���f�ߋjz�&���i�4�y����D{��Ih^d� j�l�A���I�ߛi��t�ڇ��?����ٳ���e�(�Y\G��@r7�~cySZ�!��f�W ��Z\�,��py��<I\~lٳf1��F����ȉs'�����Ľq+��Rz`�+V�լ!���ֵ�C#P� ��u4da]ՅG|�2�f͔zea��a����@O�7�CL��S�:��`=[T�ҴۍJ�OF��3,�P�^���?F���t_0E,�d�1��M�Io*��1L��MvjP�Z�f͛�F�(j:��X �@���3qzV���#��Z��ʥv�����+kw�a��H�1OV aI81FI*�HAd'$9c�;6lٳc[���e�#i�G �*�r ��Ɉa�*Aٳf͑��>�^�]� us$w�W>��2�4�.�IQ��0�6?6lٲ�$�+���P��[�N�|�Oݛ�J�eA��厸������3j�t��2�f�r�`}B{ {��������|B��C53=�����W��k�� DH����s���R2}�m����ٳf͐o=��^dдkYV�S>�厥!�$�D5WvV;7A�Q��+u���h~�ա��Oo����s$��t��k� �x��/6lؕɥ������q�-/4�ʩ<��y.��H��S�,�2j�zq�2)� ��x�̡��+S��үt�.����K��X k ,����VFn �o�... ��eZ����+��6�Ϙ"��?G�����w�^ZB�����Ojq�]�x;6G�0'��ɺ���[��� �s=q���y][mb]<�_Mc�O,u�����W�,�w��F��/�:.9ze�͛6j�w�z�u�g���M0I�䢛��aE��0�Ѵ[�, 꺭��\i��m���/J�Ad �W�y͚��a���H�O�yK���2�+�)��#_���8@u2i�~�|���Km9�D����ⱁ��o�V�U���C5�w)ΑڙfoLV��*-�¸d?5#l��Lvll�,h�3T�7@�9�|���iw��:���V��kbi�����X���5gZta���)�r��6lٲ8?2<�d�!�+-�}t�֩N��2Ϙ�^�>��N�R��Ui�ֆ��0 ����)�:o����֠�>�k&��,-f����m%4��F希�f͛6r_1��O�k�g�\��]ZC���i�b�� #����Nt�Y���{MZ�H-o#���v�ji���f͛|��+�J����o�g������0�{�V%%½-��?1��u���A�}*T��;���y�1z c_YJ��IZo��-�X4�}T}�{R4~��F����{�l��ː�<�h��jK%��$K�C�,��U4�������d�okk��=�rA�]���s��x9'���<2C�8���J����v���������������qq�q�u�`�?���q�P�{��\�q��6c��(ֆ�j���^��g�.�E�n�9�ֵ[�����]�S�J� H���6lٲ-�,�W�Ɲ��W�ZjvJ�J�����n�b�c*ܹ�k\/����/�����ష������p�x��C�����ͺ��e�j���-��'�au��%nQ��[�(�:=�������x��5���^�rX-zT����6lٱmkR}�z�Mj~{`_N�.,��I�M/Ր ��� �Fހ��ZP��J�h>S��W���36�r׵)�)�~܇e �Q�9�f� |3�_�_y����l/�O�u� �Ay�u �V�Ғ6Ev$W�H���j:�o�]\Cs��ld�]_�_��r42T�����~lٳa�t �n��� �m}kx�@[��L��{�Z &�<�g�#��6��n-ٕȉm�4ezu-�S<���iڤR̓6�������,Q�ԭ7�h�A�,-<�����^����eGau��T�B���|02~^k�O��_Y�����D��/%�[� Y5!�D�i�%�^�_���\{�2�L�H!��)�d,yV��������6���O����/6l�+6��Y�D�/uk�y!���x�s�Pۻa��1 z�H��kl��O.�>�;�!0�)S"G��"��rU�͛6l���M!��}.� ��N��]��ayK3���uӦ�N��E�r�$�=T��Kp � j�jОA|�L�'�n���� ]!YBҤ�â�*@�U�6��_jf�i����.l�i���:����=)�I2��6l�As�'���G������1n`���>��p�]�͵Ν�_y_S�� �k;�#Q 1�2��񏄕=FH��3�w���6��C��3��y��h(a����+�B:�V����%� t-��p �����O;yE���&�n��b���9*�#���\;�/L��@=;� >X��յ=J� CM���Մ�P��g�U�dt&�QcS�P��̱��6lٱ�0�[�-4K%��I>�-��/$���L�oQ҄�MH�Xj:��7�3�ͥ� !� U��"���ٳf������������h�l��]�fqx�u�z������N:\�~lٳc[��^s�u ���Acu8� 2���������?�*�X� >�m����n~������v����)��E�T�'2܊�... ݱI�z|f+[�<���,�y�f#O�{��\f�?����86lٳf�5��^�<�E��6�kz�ޫ�i�i�ݘӯ`���&/���vP��5$�����F�t��sT����N�mg���)�7�i �q����&��f͛#^e�֯y�i�։{��d� �y�o-�U�����A�,�?%k�}��圉���T�(�P%RJnLx-]��jd�6lٳe���^��9ha4�.�J�D�RЭ���^�̎�H�#�ɛ����|�����_�Mz ��G��!� h��^mꂦR� 0��~_�5�,�na������9�Gx�[̒ѕj7 u�O���Z�z�ֳ�ZZ���Vf�)R�ZD�NI!y 3F:6Oɩ�lٰ��]�^�ͥ����a�n,nH�<`�.�Y~#P2=��T�g��E���5�%�Um�Xd���N �XV��'c�^lٳfȕ��|�m�_j~]���MO�{�}N�Y��!�����ʻ�Z���/2$0kw��T�ё ���^�hn>2� L�^Ƽ��6�n��Z����.�`x�u��U��f���\��E�W���k����f�"kX�!�)$�� �ҳ� B�$�OЧ�|�c�O2�Kh��<`��)� ��Xs�6�l �4�� �B��'�b���AŸ�އ9��姚u=.�K�uk m��=[ ���.y+r�JŊ2��Ft+!|-c��D��G�d��>"��-zT���f͛63у�GS��_�5� F��Z�K�����h� /��8,��ԊWlKB򶑢��[Fe��뺌ǔ� ?nB(�?��|ٳf��������B��{X��-��3IsHKK�I" �* 2A���A� ��n"���z62F�����r4i+Z�a�lٳf�O9������/I��O��3s*����%Z! �&�I��4�-�����2M��m�m��be�����'�#|<� �L&s�M��ˏ��FA4�yz���.Ԧf͛6����?������͛6lٲ����푯.���X�&��K�\i����̭x�!��I�������5��ln����9M���n,b�����TiJαIU��j�45풌ٳf͑�7y�T�N�o���sy�\u�܏ ('��:+��]:`�)������I���EyЧ�� CBԬnʼnQ+�I$p'#��ʌ��NINlٰ��Z��~]�5h�Y�Ҥ��@H�`+y�S�oo��Z����ĩ-g+Mn��y6�?hq�2I�6lٳa3y��˭.�u8F��#[��͗����w댴�/5��muX&գ.�I� {�Q�������-�;�f�;&N)%�Fzr�8��0"y�ɇJ�.5�s�=wV��/٭~�5�5];U���N�K�9�c�:�aZw�ٳT �N��/��05}KQ��Pӭ���O[�Oo3�*z2:V�]QQ[�4�;�'Y�f͛6l�]�kv�-���$�R��@ [�A&y���H� �������g��qk:��T5 ����f͛6A��?j�~�{zu��F�5�72�d�nb2~����2n�0  ��7�͛6l�S�t�*�K�J�-l⧩<� 9�넰y�EԮ,F��Y^[�]}R�I@�&�$+%�b+��?��A�v���vZ��vdZ�,K�G�nǦ���n���K�����%�5���dM��P�3��+�p�6l�#O�{��\f�?����85Fl����3���<��8'��զ~���������Dd�IY�;(UH7=r�̶��En��}[�k��Y6"/\ܬ���Ǐ?L��3Tf��ʨ�/�)�jZW�;��+��;�,�y�Y��H�Wf@����_�s5�>e�~�mw�k�kk}�kYccmd���dZ�#�m�*�5Fl�ٲ����I���4m"��� �/�d�����v�K6�[��EdHYxn��-�p��V����o5Ccv�5���jK�:�� Ʌ���+�=FI3ĭ�e��k����Co�/��n�F����r!����ƻ��ZE�v�i������qq4��"���;HȨ�Y�c�Q�/#���/�&�K�I�6W������>��@�s�6?,�i� ���{�+M��vr�#C-��r�sy�є1��OO�rNu�C5F^lٳm\�yn�s�:�����l��!_Q~��c�r��!�]�i�Q�z���u�����Kh�Ә�YDr���N�ɿ�?��MCV��n/.���н��w��0Oب_�� S@�4��-t[4����� aԍ��2I��e��fn4������6�ڣ���5Ժ�o�M颒�)�F��UFj�� �-�i�k�2��и�g4Q1S��M�g����FTҴ�N-f����I�K"oV9�"4��R�_������{i �)$p̡�h�)�� є�^�6^lٳW##�L&�O�&�}j��8��c��qޕǕ�����^b���b���a+H$+�# t��0�|��[��c�0i����U�⥚��d�u�tꬡE{d�6lف��9�&���I}e~�i��h7��Ksd���^*�Xz�_��2c�dd�ɚv�qo5���o#�7�zɻـ��a�J�3Te�͛"�������/m立���B�P&�6IC,�����#��r�ͮ�^`�n簑����d�~�5��–�%��R��M��?N���i~y��=��͔���%���eU�%V%jT��Z��7�t}Yt���u n��(6V���)���r� 9S�uz��ٰF���A�����u�_9�]�M���,�k�Q/�V�.L���Y���iώi���t묝^����B1}|_�lBΜ�a�4�#$����� ���ĩ'��)%`��jT���80���q8�R������^w6\>�=PJn@�����M7K�[�Bqo �(� I�G� ��`1���W7wv�K��ő.��ÃH��T� W�k��n�D~[�#���������Kb���p�4�d_���'淔"sk�\ɤj���Z]�rI,,�edhX�%!�~�-���5�6 ��zF�a�ӵ�I�^mjY!��8�F�&��uJl0׉��r���'0 :eП�j�n�i��J�[[Ḫ�r�D'v`0aF��/���#B�k�Z�m-��X3Lx�;n{ �&��� �i7Kwf�eP˺��p�������C��R��6�;���7�Z�|��9�sP��r���9�sP��C��5_�JWo ���7�Z����*�5j�9u�A�C��5j�9�sP��C��5j�9�sP���J�e�OS�C��5j�9�sG�_��Tt4�C�׮Uj�9�pN���A���?�-��ҳԴ�n�9�6�6 �E�egoU�7�J�b*��v�_:ZK)��TRZhtЀ... ��t�u/(I j����ʱjI �"I-�������7���܏0Xj����յ�_j�6?�n�y�`���Ie�'<}62 ����� �h�e�7����[�dg�n�E�2x�A��j�i�u/=I�h���]�..

�^0���̰poP*�"y 7�m'�u�$�:�^i6�5�FH� ��c�E7YOr�����֬�pk�VK���{װ�L�.�HU�#թ��<��~dMq�k��מ�ڬ�Z����&P��6^�b&�G3�m�_�,��;̺"y�U�J\��h����E�~��Q�A"O��v�����5�8�[�!u��me6�,��{�f�T�c��RJӨ {}� �.0j�6F� ŝ�]���4�Ey'�c* �HZ o��~A�<Ǩ��m��H�4K�V!�ci �=�(I��%��i�����+{ �kS����[v����f�'���V�7�M+P��v����w󦉮�[���M$2�]��澩F��=��a�Gy�N�<�u$v��*t����\�xϮ�J���O��Y�ߠ귷�&��A��4�ǧ���M���}R�O�>\!���>uֵXm��ynm ޜ�5��Pzr7�8Ƨ�ٶٳ��,rƲ��H�UMA �~lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳ`�?���q�ڇԿ�R�������_Z�M������I�����.�����}c��=1O�p���;aN��������+���+������%;�Ó�7�"�����W���W��zr�_򽰏�?��K��ߡ=J�����.���?���)����*���_S�Zzߤ�S�o��>Uޘ�C�G�����y~����q��b��[��E���i�#��V��!�n�����~F!����ޗ(y����OO��������l~��#�L^��_���?O�����|^����rC��G�Z��W�^~���W��G-���9�� �ߗ�?O֚��)���k�q������?�����o�����������^ަ�����|����G��7��������ˑ�<�u_������~��G��I���~������g�k�����o�}�h��>?�z��oѶ�B�~�p��J/��������EzZo��#���=_�?�O�߇���o,~��ݟ��*��������+����2Wژ��ѿ���������=_�zu���O���^ٴ�џ�4�O�g��?�=zr�������~[֘?��D�_�9������Q�������]�'���_��J�����ߟz���W����?����>ا�'�������y����G�<��D�#��s���O9��?���������o�O�?��7�'�������y����G�<��D�#��s���O9��?���������o�O�?��7�'�������y����G�<��D�#��s���O9��?���������o�O�?��7�'�������y����G�<��D�#��s���O9��?���������o�O�?��7�'�������y����G�<��D�#��s���O9��?���������o�O�?��7�'�������y����G�<��D�#��s���O9��?���������o�O�?��7�'�������y����G�<��D�#��s���O9��?���������o�O�?��7�'�������y����G�<��D�#��s���O8��վ���Sׯ�6�~�� endstream endobj 344 0 obj << /Length 2763 /Subtype /XML /Type /Metadata >> stream tiff2ps //10.91.11.230/Womat/Production/ArtFinal/0000000053/526815_1_En/978-3-031-14196-6/0005446564/526815_1_En_1_Fig6_Print.tif endstream endobj 345 0 obj... elax .1.2) /F 4 /Type /Annot /Border [0 0 0] /AP << /N 625 0 R >> /Rect [95.04 336.87 100.021 343.595] >> endobj 347 0 obj << /StructParent 169 /Subtype /Link /Dest (table.30. elax .1.3) /F 4 /Type /Annot /Border [0 0 0] /AP << /N 626 0 R >> /Rect [121.32 336.77 126.301 343.595] >> endobj 348 0 obj << /StructParent 170 /Subtype /Link /Dest (figure.30. elax .1.8) /F 4 /Type /Annot /Border [0 0 0] /AP << /N 627 0 R >> /Rect [71.28 288.77 76.261 295.595] >> endobj 349 0 obj << /Length 10 /Filter /FlateDecode >> stream... ��a��6Z�����U<�7�)��$L 6���8��H�-���|S[�A�۔�IJ����������;�5�6�>^���[�7֢�?Ji�ѭ�\��(*��<�L�Ѫƿ��*��� ��?34���� ȓLU��r�q��gu�$oݞ]:gz����4�&,z兦�s����Q�,,G~_ ֻҦ�r�}�ߖ�a������<� )$%�m^�_G�r�HT&��j��2H�t���khɬj\ nb���Ԃ��wɵ�����k�y��/�(�:"�B��8��������O�aZ`�#�f+y ��[�M�*��IG��&�;v��Z� ���L��M-,%�-t���0��*If���I��C�12��K��"���5?=�W��u/��r��M�io%������+{w��Y$V�Rޟ�Wo�����ć��������b�{Z$W��/Ym�_Y̫� ��������=�0�}�ۏҗ�Y���M>�|�h��V�>���h›�5�գ�����ZD.e��S�iB�xj��Ҙ�r�z(�S�O�����n�+���H5 ��_�Zz�� :o.����u�׬!�MGP��NO L���C��N����Z�N�P0��(��J�Q�����5�ա��#{$vh.�g�II��RcÛ����bֶV�5���7���]8�1�P9~%�k�(�7SX\��Z���&�݂B߸��Ԇ$v� X�Z��2����7�(�i~c��n���h<#�8��4��=?���D�_�>xO�x��e�8�!w������_6"?���� �l[-~���}?���Pb����)������\�H������&1\��C灴���?֓�N6�����/������G畈�����p��x���r�i���b؅����=!����S��7�t#����͈Z����I�1g;`=D��s��5�N~6��mq O�m���Ƙ�9�������b'����#�i�'�*oՂ��r�,��>?��'�M1Rr��-�w�1R������;���'�@��?���E���/�+��ְ傅��%��o����c�[�F��e�d�A V��4�\y��Z��o�i��J>�}U]�G�PuٖH��CB2�ɑ�K��n�]j�Bg�۠f� ���IS�M0�R����X,���<��� q$bY'e��"Vfju��,� �X���XE���� �x��J���O;蚅��s�Ӣx%�)E�3hdZ��S��������ДaU$n ���E���� k}<C��*X�����_ r����U�v��a@E��T���0�k�c����p���>�1�,Q#�3�%2J��* �������n�n }kQs*��VJE��0�Ƶ���s����g�9�C�"��FV`~`�T�}Z��yZk�>���L��$bxdjPU�"��0�����Ċ^F�Uc�a&�${f��x�~��E�P����AF������M�)�镂���Sқ�6�d�L?�b��e�,�=: eq)<�1�TT���0�K�$��fR���R(UXR$?��|�~x'�]��������)�-�՟��[��4Y?Ս5k������/�~�-ѿ�i^���g���0 �'�'Lz��������g�.�A�1~����G�����m�e��<���0�1|B����������K��bFO����-��<���_���|��C�T��q�G��� ?Х�a�\���W<@I���Ï�8q~y��{)�%?�����!��o��q�a���� ��K�����`��&������-e���bd��z�MH����K�\��o�ʮ��׭ԟ�e�����{2xM�1��Â�5�㮈�|���\�'/�8F�O��0����j19��(��V�4��tTE,�}���l�M�0H�[\��[̄2��/5~s� �w6w7�Y��%�8m���Όʞ��2�j��F�_�~H����*�y` ���"g����>[5?g|�F�.��6��;�.<�j��$���u>�4AE�!#��:���� t��q�-�d�ف���F�*�`���x���cyf6�i��c�S�,�iT����(n�L�/� 7Y��>�d�/Ϙ/o���e�֌L#T�F��U�$�>Ԩ|Gy�FKo'\��y/m�/*�$��Q�j6���S�)�x/�������Ki�sU�*��wWVYN���,����z}�4w�4-:�... ��g�ޛ��� �h��` ^�iu��NQ�(Y~U{SA��-�[Eic�Z[Z�8�iwAT{���m�m��8.�C�ݓ�15�=�מm����w���͜’��m� :x�Xu 7���4�I,��� ��U@�䲺��9#��5�9G]jv��sM�=[k� CV��� �5��f����Ȋ�[tؐ_�Æ��:���*��݀�`1�n��v����m�7`i�}��<�嫻Y-/u�[�Y��}6�)��j��|�a�Igc�ږ�S���X�Mu ����R>q��Z��z�r��C��nl���F��*����j>�~��M8���}����E&�̶���q��F��$ �� �4ۺ�����Ϛ2�_�[z֠�6���©��������U��#�X]q�sE����P�0�YZ��4]N�]2�ZU�1�]���~�v �� 12�$5���/;�1Ƒ��mR8�X�t˵UP(� ��Ό~ϙ-���o�k���mU����Uݍtۿ�bk�{�MG��,ɬ��ݼ���"��X���JA %#5�1_E�74&��K�z]�քV7V�Kˏ��qJ���l�՟q/��58ao�?/[����`���% 1�J���� @(�z�;y���ᷟ�N;i�\y��h�y~���� >϶!�y�BgMR z�Mb�7[ZX]ij!��J�6�lw ��#y��#THlU��/`2j/%��L�iKa�Ifc�҃�}�u��tH�@�b�D�J��.�� (���`��މO�I-��y�4�>w��)y�ތ�(4ۺ��)�p=ϙ��pmn��V�X� �G�GNKF�VXٌ.i�S�o�7�4�V��+�QmF��k���l��|�O��I�� ���C\E!�%�*��wAʝ~�� ��>d����w�4��Z1��Ko��ݟ��K��.�Ewmw�(��� 6�qQ�j����W��t��S��j�VI����,��Ij��N%T ���x�ː�]��F{y#_1�pd*t˱�(|;b�� ��n��v?�\����%���o?�A����H�d��3+ 6��\/o� ��F�Z_��Hs���+�3\)f���j���'c����G�;ePQ�6�`6��!�ƌ�������w����[�w����o_�f���8���CE"��-�$aA�]��J����=����Z��e����0��P�T������ ξ_�$�1[$1(H��m�Ȣ�>φ%7��vhO�����m�� ���/��J ��޿�ͻ��q�y�F'��%���m���p���Z}���pk�Xk��9=>낼j='D1�O& ��6�_9�z��+h|�n�‚8��u�QN�jr��ƐI��[`7��e�=?�ʴ��H|����vH��>�*�{�O2[�:m��ӑ�3��C1A}�G���M{+K;�wd�C*?#�ݿ�p��_���t� ;�`�]ۖӦ�����Nagt@�E[:��#�V�4�Ӏ�jMNj���1��]zK�r�LD>��q�t0iX$|�஛���...

�̜�j�,6��N�ߘ���[?���Ef���U�]��`6�P�֗��ߑ7����r�����x�Z2�,l�,���©�w'}���'U�Q��o�h~���&��-GZ0"�+�r� Ws��?�=JO3 �M� ��p\�IJD%��I> 8��vn��ɇ�/� ��j�J�.u(�7_T $�=:Bz�ʍ���0��^t��� t���0�&�J�\�Z�A!3�����ϛ|�h������K�#�z�Xz���z�^5�N�y��s��vw�4&��0���ȡ�׽+�}i ��s퐨?3/��?����+��O��9H�����QVM������-~���sV�Ӵ���x>����_HzI�H��m�A���l)�f� �0��Y�h�p�e�]����s]���S4��~��y��W^]���؛�{�Zw�g "�T��eM@W�Z�v�7��k�Mt��6�\2�����`�Yy r^��éZ���2IτH����X�����s��P��/����������w�+���� l5�*�j�����Z�S%�Z�Q>ެ䩫4�����A��.�5���o끵?7�:��wa��]�$ 9�.ȥy,9R�+����h: ������O4�q-�ս0K��U�U@�_���|n?�K\ �]��U�Xui��m�U�?��K4�G4,���-iю�>yv���z'�ӛ�{�����p���G���y��U���C,vb�P"і��X������ <�y{��?�K\B�;T�,n,n�Y���h��[oQa@J����ygX��t���wst�B�ո�"�AU��0+� O�|����$�\%�F��y����=N�O[i~�XZ� H��~&� |�����QF�FnDq*� �Q�|8��˿�q�"�� K�.[y�o3B�C7����Y��X5[�#�����.�5���o�^y�B�����{�yg�H��X 1��P�rf��|��yc������M�z�!���E�ac^�󟖭- ���J[Ɛ�0������_?y|0!�9�}@=�_��:.��A�O����2�-�Į^��v#����ӶKǾ^�k���� ��1���v������3L֞�%Tt(u�"O�����;�[���u"�e���i�"ُ.5c����|����!��F��4o1��x���IB8a���VD.�(fpj��۾H-|���[X-U�X[�!���^G~��,�~��ubn 4��Ȧ�o��kp�W:��S�Y�H�R[vx��v$��6�v�W�����q�"��g�u�#\�~�k�O����I3�z�ȡ���ݹ^����-�����W�y2��2���R9a���˽���D7����.l5����Z���t�Qn� +��v���+�CN�q�����u����ck Bfh.Q@.@;r;����/�P�!�e�c��{�#�Y�Zj67��`��+WX#Ӗ~#� �G4��z��{����� �p��m3T����P�N�+��}w��IoM�vPj�?00���/.%��R��{�Y��# �I@�~ܒ3{tÿ�����D7������^a���n�C5�P�,� ,����-�R3TV�A׮�m�曧[X,�2�Z1��j�7g�;rbM0R��ˁԓphA#�?�"�V�}��g��k��5���$�X��y%*��&Y��L�>�{��?�C\/׼ǢkZL�d7��5�ORv��TƬ�(YA:�/,_h~^k�'��u� ���"��*1�Nſ <>}��v���... ��M��kY���je�,���r���� ���k� �=�����'�D�鍒X�Gy\Gj^YEEf? 2?���Cs��E�]�_�d�τ*�m�����=�����O���in�Z��F�U��yhY��ŸX����|�����`M4�N��T�ĎK"_k�H�r��y["� Ԁ��qA�K ;`{#D���������ˬ��}+*XQ��tkII1�$��F��чD�a6�wq�������m�؀�d��'�F����5��V��[C_J�=HQJ�s�� �y��ٖ��b�Y�Os���qi�{2M� 6O'�c��s�yZ�/�4��^ 9G1��� �%�\_X�V��27���)�O��1��'�sl���#�4��^��5������؅�ٟ�b&��b��=�������x#6#��q��_�-�����R�ضl�K?�6�������i�i�n?\X'6��z����'�Cɂsbf���ba��Q㚣j_� �8�����G�r�>�i��� ?���?Vl�#���ߨ�:�s�� _������~����:��� ͈Y}���"o�8qGe,B�����I'� )��~Q� :x��3��,̃�*�*j~A�t�������=�G�j�M���t�.d�#�켕�~A؃���9�|��v��� �s4��bb���^�^Njy��ae��䇖F�����{��zwVRD�� s�& '�S�*{�㬿?�έ-���k�{[4����W �*  ԡ�J�\��^z�� ~���}E[��ّ/� �͢ X� �r�`N����`�Ե3��/�jL�i�B%��v5T�Vj��.��Ck��� {�&�M��!:{[A�d��DTH�ʠ�nN�3����]��i ެ��W��%���di`�. TO���@���y+]�Q֧�ɮ�,�+���e�һ��)��}I��󵾑�����q,�iiQ�ZV�/�,]�W�Uo�q;O����1G���k,����5���Տ/��U ToGR�i�ᾝ}m{omyj�%�¬�:�o��5��y}.��Kp��h$�G+�+�#S�\N��ZY�m�;F?y ۜ�yH�윓�0=��r��y����o�[�m�����p�Z��k) r�f����CN�Es�+ۂC�����M4Hg5�nP��=�du?�"�W��-?���V�_WB��c�ɋ,��D�����b`��ڡ�@�ncBڥd��S� ������F���O��1��'�sl���#�<���������X{���3��D��,_6�����3����f�S���R/��͈���\��l[6-�����o���6�@� 4�1�ܝ�8�"�r�2�tr���o����5m1�$����F` ʢ'cvn+�ݲ�Y�R����!�����"��ಯ��? ��ߊ�r��i�Y����kb��B\�$�~�5# �?6�R��D��ukh��������='s �v����fڸo�/˨Qg��-Q�%W.$P���?��B�]�1�/V�����N2]��� ���|jJ�j�jW|k�i:ޙi��+wb��B���f�R�Oj��q�q9D��&?Q����\�h��Q `]M��m燡'�@��B��?V7s�����8���u��/�60^9>�����z_�s��7�L����9��"�8p���mg�]VteY�ݭ�˂A���1A��K�9����Ǖ�������Ky����\�� B"ł(��q4Z���L����bӢ���~�2nUyZ��[���T�7*����]��Z�k;��{OѺ:�)�D$pD����U���6D<��(-�G�״� �o�ý��������� �>�쌔\G�i����5�ii�B�Z�C���yYM}"�RM����kJ�tT[8�M ��Hm�(ē�|pE���i�\���v�p�wo!���ԌM~&�L_�~�"�_�)�����af�9��]1��xO��T�����aה�ro�$Ԛ�(��t}f`��9�0� Y���,b��X,��7����F�+ <�<��Ze�����HK�G��!I�S٨��1��A�1�۠�T$Q�EUb�«�iڽ��b���!����%ʂ��xV������)� A������k�_R��a��P��m�H�>�����h�j���c2KӜ�2�����8d~���)���m�ҀE���A��~#;����5�+$�񪗑�D�ZGm����5�C������´s�%]!c_J���Ϳ�c�_���U�Q�Y��v��?���jA��h��WX�Mf>��k�Ɗ��LA�R�M��m�[��͔ܦ��,b�3q?!z�1�/�ж���f��'�r��y���Ť�cx�A$2�Icm�# 0?1�l�i��K����{��l���ᚂ̖��k�k����m �H��Yٮ$�i�Ey�v8`�27��>j��e����͡}��ٯ�P�Y)�l��ִ�rRKk��E4e"�����*� �>o�>{�����]���%�OoG��f�^E%�%�cN$�����_�����W-,������D|��!O��1��/S�c��H�)�EQ�e��@��+�a��M �T[ۦ]"Wv��4B{pT nj��yT��0�����C���mO�o�����V)��&��k�m5-\$��&5�Riqk�/�w�~��?��?�$Z��y����m c�G6��7�-�-\OxF�1-0,ͯ�}$�~���������I6��^c�k�� c�G6��7�ST���1�5JG�}f�o�O�������?�$��Lߥu���O�I6��SMSW���hs+W�6�P5?o�+�WX�� ���i�5�U֫��=?�*���`Қ�����������J��?ۧ]�3����@���I��ա�)���8�wI"g���+�ҙ Կ-u mS�o7��;t�LG��mV3w;�.�ڍ�0�vm����,_��&��X�=��%5�.1sp 2--�ġ��2H=&zҪq[��?..���xt-E��K��ѻx"��ub$�ҷ� �ָf��C������d�/t֊���w��$,����Q�����w�����\��K��F���X�fH#��G%�ⷼ����:?���W�\]y�Z�'��3+�:���M���-j�yi��¸���+ oʺ������m�=&5����x�r�F��Q��u��|�g�(�I�a���w�[�.g�{f���7�B~��e���B�cu���}KU֟��(�4+-)�`��2�%��F��$����~y7�<ìyWG�d�d�K�H��xn-c���9T�è,:�k-g mtRc��CO�/��� :��S]pjv�ͧ�T���ֿ��9���O����-OY:u�: �99�� &���/�SZ��p'���O���^e��ǖ�I��SB����ፙf����@�,n�P�o ��~�_5���}}m��d���S)e%գ�Q���;��|�u��sK��� ��-Ӄ�Ų��2�g �^��I��b���m�rjz�%��15}f��k��f���B�8��������k]��Y���� WY���IV��^��5��b4)�z�Eՠ� F�:��b}G͚G�$ӥK�,P�kެJR�... ��k6�K�U h��P�E(3�y�[��Ϫ�g��t?/\E;Ga���i�a ��_�U#�����Wc��C:��� ѡ����b鮌���V0��ĄE!o���Z�P�O��������G�0w���[R@Ss$�B�Y��3=[~ZygW��mt�G:n�u��|�w�p� m6ƱTS�z:Nto+hN�wye �\��K;����3BŘ�nMБM�a,��Z]��i���)� �}g�]�J֓�?nB>$�����ªi��u��|�<ɤ�isa�y����:=ą.9FG`a�|�.q�T�C�7T���<�m�#[ϢX 2�Q�B�+bE,!_�&*)#�D4���.��_�k "of�Iq鳗!�54f߈� ; 2�$�{��=9�\x��_3�mm�֣�ꚵ��t����5- ʳ�����L �Oq�jk�j��_0E+�O���4�x�Z�>&�}��q�IFlz~?�&���� �B7a)��rsy��4#Oqh���O����T(�>�kJ}��1�ϙm�c��<��)_��|RM>��W�b�3��cۑ#K�bӞi̯y�ܷ+�V�X����tT_� ��XcPUc�P �V�o�z֘���t���5�!`obP�h����3A"�7�_�8�>��{��|Ѥ�z�����NK��Wֱ�g���l���1 <��Xi����2�뉑/@u�r�I�I�����%x�Č^6j��a��o��4л�=ͯ֕K\#\*�����wUq]����n��������r-��$r[��xe�M� �$��uɜ�zu�����"EhXߚ�Q�C8e��!� #O���;�U����OF�X?� p=5e���6��k>}�E�yt�}gv��� w��_ݟ�"�����;�O������V����-Ț(�y=��uW��,m̻��QN�/���;��f��;ݷ�n�qo$dq�KD�GEP������y ʷ�P���.�+���O��L��K��F�IP5>�t�LZ泠���?Hi��m!Q�����(�ؾ�����tm:�Ԃx�mR���T��U!I�Թ��n���8��(�c�9BE *��8��0Ur�"��*�_���o ��� �PV;{u�$�1�n�w����>[b�M��٤3���ԙ� _P�� �~���P�?U��ց-�]�h��'z���Q�+�z�B�Rc�����S�Z�Z~�� ��%�8�7�ݧ�\�ђ7F�DE"��6�YQ�� 0�O�����L�%��ٙ��F2�9f����~����2���i�O�^�����1Y���<�L0�a��Pġ"�EUE`}N�� Q8��6X�zGp�a�7�~ˎ�H���/�U�AǙ�e���&T�3N����m���*�ՈU��rO�a=���CT�yu(�D��)l�E�[��f���p�V���:�-V%ڐ�mY��������$�˲H�~㌳�x������Z]Km�.�Gֽ;q[hX�_��R���M\|��I6��4>��RԮ4�?���{d�j���B�� 0;��h��+�I�I`��Ř���e�b�TrL�� �P��)n��8|_68c��إ����F&��G���{`)�_��ׄ�Z+��W�����m�0�������e��C�`�x�����COh�x�H������U��Y?�B�b�TQ*Q�lȷ��0u�+��Ɵ�ku ���K�Ȏ�Xu8�� ���ß+k7Α�ź���J��1u�����w�!�������ב�/��Y������c�...

}e���e8�������Ψҽ�ֳp,�*&���[Al� 6�8_j�����藶P��ɭD�4���X-�V幕�Ez�/JZo�}��˾g��͵�i?�Z�ŵƕ ����qHd�������d�������ĊB#�<)^4��w��>�m�|��;͑�W�����~[3Ohg���xՄ�S� {�c�\���f@ �.|����y2���e��X����;i핵�>�qZj���[�i�/$k\j��Km�I2��������7�=C�pG�Jn�/��%ѯ<�5��Eg:��{x4�Q�v��^��]?O�����{k{D�R6GfI��#k[ZFi�>��Og ΢��S_5�^��S��1�[L����I�ը��P�z፾������KMU�R���aiLdW��9S�"~K��.��� ������=�PE �E7�RG�I|��<��K^�?�E��&���ԫ*� �+ˮE5}Nk�7yk],� N�鐞���2=A��S��7�ZV��k:e���49V��@d����㪟q�,y�Q��^o��fҴ���h��}X��M���:7�?�_��^��� [�v {�K�w�+�Ŀ9����w�Ri� ῞����Ga3ܑ��J�]0��~d�����.Z�K���ִ��ݚ�P $(�q�E��~{�O�?7�]OA���Z��rtmH�-����a��? ӈi����{�F���V���j۸K�I��"� n���8.�N���/|�}������@��%��8#p7*� ;�-މ}�]�S� q�ygL��ti$<��o�'�ZP�"��ū��a��?7S\��c�ꫢ�$RAym��e'⍥�@���?7o5}g�9��(գ���j0�X ���|;�������/�A���� e�o/5 F3a�����<|bSVxfF��ju��&Z���\yO]:���i'N�t�#q=�%�re��rbx��x�9M���:y��X���K�X"�^D����,��+�����]�#G� ����{0q�,�4�h"��?VgH��1H8�.�̼�m�sy3��z�M{���-v�N����FaV�h��wUI8҆��[�4/�Yyb�ɚ�!��+�����]I���J����M�-����ե���ʊt�CL�}X.oi*\0������r�#�:M�hߙY��K����O�}Q�O�Gh��l9w����s� 1Y�;B��B/"��9a�Yd��xF��X�_q�{Ӡ�U���kjQ�A}4�:,6<� >����W�m��� b��ʺ݆��Gy?����L�wֵ�Ȇc���5 N�����,d��yY�� �e�B�]֡QT��L-�|�?O��^�*&�gw(��E%�FQ���$�򇜮��1�����%������5V;~�>t�w�i��e֭�. ��`� I�DZ�GWv J��k��<����w7�u++�+�O��$Pra�S~�/�uO4��C����� g��%e2r�y[�k�Q�>��&�7��Ff����ʩ�FIY����?��7�Ww2]Ju;%�$^%x�OIEO��S�gg�?�w�[��������ɶȥ�H����i7�e�mo�� q�`�S�i �C�u���B�7�u�KP:$0�2Kmi&�wx �DY�ekKbՎN_ �PP��l+�>�ce��)i�4�]j�]M�_]Z{�� w�� zЧPxa�����<�u��������{��T�zRQ��:���{L�|���Yɦ���Y�U��T����H����Oa�����]����eAm�^����n&�%�6ߠ༺1�5}W���zi���\�}��n&OB���sW�V'��R�����3�j�l�� ~�$�!�\N�]Tp�$F`Ht؍��˭߽Կ�p�� E� ���d�� >�L�rBA_`���m�7w�5�[�hl��n�Z��b�U�����YKlw��*m��$�S[]R[�\�"6�.³�>��N��A���w��VZ�\��eg�kv��3C*�˄u��9D�)lw����EO,j���^�6���-|Z[%�%��8L�cu�!�� /�'�f�γ�"��]�$�V���ܫ4PA"=�f��S�r��ϖ��R�ߚ�I��P򅮝�˥�Y *f����C�����j�ˤ�c�wp�~m���y��J˩^ ���B4��X`}kɺ7��^��#���7�?J��ܒG$sM0*�H���j`��t�S�7���:ͤ7�����,v���6 �gH�I%Aʧ�����o�3��ޱ%�,Qhvp<1����'~`�i�{�y�R�E�\Դ��6:�� �Ŝ�Sn4s%����H�ڣL1w���� 'S��~w�m7[�}kf��7ӎ!j�?�d�Tm�>d����=I�l �Ri�V�ec$�%��$R��}XӋ��|<��o<����򷳵Ԯ����+����n9���{ɷ~s���:��l�m�����▿W�O�� ^�# �������W�\�Gi5��q�j{��'Si'� 8E�*nƵ8�ȚU��������X��\��Rf�k%2BD�sB�Ӭ�Z������F*�ۤ@F�7�n>�ؼ�{7��|�q,�+x����;9�N�ad7N+lj��p��V� ���o� ?�VwMƫ�F#�4h�U2Y�hX��ONF���f��Bփ�~�{�jnK ���$�I�cc����5����Q��E��ZG����� 4D�^Aˊ�ކ�+T���O>����g�yH1��StE������oFV<8� 釾pӴ�������ސ��d�@K�,�|��伍ɺ��bW��sy+�W��s�L���b������95�l$�f�l�h?��e��i�VMN$�o��G����y��3Y�N�ui�Y�i�%�OR�K�H��o��;p��N��_����)�me �Dww6 '�'e�U�_W=i��zo��)�z-����Y��o�����/�i���'*�)�� Dw�UPI�ޣ���̞x�s�/[>���r<'��.���ݐW�?i#�S���/uI�e�U��A�n:L*c�c�_����R��ه�!Դ�7���b��6�yN�XЅ&/m�F��n5m5�����ʖ0�k�_;�q�cuh�L���+KQ/�¡�. ucM���/S�m5�̭H�RJh]¤��ռv���^�ol����κ=�iZ.�&� �%��O1S{b��#:ʀ��j:�cc��]{�D���SYC��]G��%��d��h�z0��(�ï/ )�n������c���14˗�����;ޛ�x����ȧz'�3H�P�}"y&���v�sDgbҭ��F�����?�1q�Pza���K�cZ����e���)$���Ch� hBF���9޵ y�\��Z�='����m���k�� $�QǨ�F��8�Y�u�2O��Aa�-���Ʊ���IEcJ�����䦞�v����K�^P�"6�ҭuٸ�����Q��?�+~� �o��+���7��l�h�WA�_��m�^C /m /�eT^+a�a@yHX��i�m jZ��s�e�Y��Ԑrh�I?8��D��P��~��k���ާY���1ܷ�Q�t�s:TVX *���w�\"�<��8o�Ⱌ��Z+�ȯ�C���!�$���d�5��.��B�����i�rv �����7F?A�����>}x�ޞ8A��+���KK��eF�� �u2L�(Aӊ�sy���_��֙�ԓ��V�<�RBv����]��i���O��dAo��-�>_2Hg��� �0Dv�zxE�� �E:u�'�-<��%� S�:�q�#�畔�&rҳ)$Q��0��]-"'��l#-��.5�s�y�M������꺍��V�u��uC � ��u'�wh6Qh �YE$Z��%���[r��h�gC�on�"�c�?74�N>��qt��?}d~�>P�Ʉ^T�`�V�t����� �I>���L*K�e��5SŪ����/��m�{�$�V��إ����[ޥđ.[�� `~4���1E���yL��{��L�P��+9�o܈�e<��f!�21�G��Ѻ]̷�x��f�o�0�}^GPѫ�"A����=����e�2^�ıh��71�fU���L�қd�o,y���N�-o�Kh�^��cy�[߅xS�q��8$���J��7�t�=�>YH��MSC��'wdA�e�SId�=�`��7�:�^տ5���;�"{+&��Ҥ& �1�,O<��FH%8���y7ʺ��[-2�c����+O)y\�VJT_��-�KsG�������-cS��D3�#��v��L�[æv_�?�WT���"���5_����V��������ɶ�m;�9�_���\� k������;�S[ѭu8�w�����:���O.$�l��6\im�K�NE�ּ�p��[¥ỵud�g�+P���Oc�ɋ����zH8� �o3�]���V�S`4�D3�0?d�Ҽ���w8^��n�n\^Ξ^�h�m�Yg�x�j,� q�uE'�_4�J��ht�qn$<斥��s�f���1Ŭ�� �EĔ#n˅ڟ����}SO��z��� QI@ZzwQ}����@W����].���iѺ���h9I���q��[I�|=bp�T��[dK�#���*J�Ӑ�x��EW�81K�źh�d�y/_��� ��7��m.�����Y���2I6�DTW4P����E!�C���M������R�i��dD�5;2��~�6 �:kQ������K��5$Va$c�a�� �^U,��|[�����vn�uaЏp0 ړ�R`��X����,�B���o##�d���p��*��I~!�B��6�Tֵ;=R�BK;�>K�c���CB�T�g�Q�n�22�����>;�3���]juVajO����&$� �N��pG�+ە��4q)R*!�{�$��򿕢����7��hv��Q!�++1 nu+zbV�W��kH�S�V�P(�tƬҦ��ݰ�9,AJ��8j�n�����i��YZ��сB)&E�4�Oz�$9*hA؍��_�]E5 2���ܖ[�cGI�'$K��RE�Ң�M�... ���3)V�VX��P��<0���M ^= �61������� _ޟ� �-}���=R٬u_'����U��K�ʖCU?ގ�.�B������Ӽ�gmc"#��UA%���q �(�cj�X�M��B��g����3����A�����6����T�C�_��R�5� ��7�-��^������}�?,,�:(�Ũ���u����˿�V�Mug��{���Rx��*X�"$ޅ��8���$��I�[Y"�JȦ�2XP��� J�A��ӡ6�o�,��y���\F��)�#{՛s�j>S����SY�U��D�Yg�����O��`ϩ~tv�:�����z`<���5���y&��tdx���D�#<�_�V# OΥ!��-�7�1V��3Yy_�'My%�<�ck5�����y l>���u ��^S����+�^�"��2��t#���料 ����ekl�eh㸍A�� ���!FU�4u4H�?&�]C�$����)B�z�x1�O� �mo�[H��E���aV4U@�:0-ϔ�2o����v7qz~����ə]�{����iF�w���+�e��:7��l����$Sġ�(P���x�1����0��Iu�$��I�p���T.$+��ۚ��z�Οm���;kq����*-I����7_��s��:�琴�vu���h˙�V��ۂ��g�?Κ��^�׭nc=z��0�����:U���>A��/��g�x��S������榧l�:����$*��%�l��䦞��wĴ�*~c�EѼ�cd&&���yz`���w�mC�_�ڻ��ǒ�o͋ٴ���6jW����R�B�����N򍥵�5��1�Pı����������x�{�k �/���<�7�ѯ�V_�QL0�@�Y��;��_�9�-����d��g�{^ˑ�e�:���2q>�~m�૭�j��K+�(�Oep8�B��e5�|@�t�)�b�A��*��� ��y����Ǒ��|������Z�U���ka%�m���z:�b�^^��ӡ6�g�,�-94��\F��C��=^����Z�̗���4��ɣ�%�I�b�@���)�_R��N%<�j8S�1�N���+����K�/!i��� �)�h� �aξ�_�7߃�ͻ�ilo��i=����{�ʺ�{�Yyg�;N�N�e������%>�3:'��H��˽��斤�����+��Z�Iq�- ���1��浄o�� +hd��#��CK)�#����_y�z�ɽ�|���ޔ�L�M^��(�0tzg�$1$PyZ�8� � ��UP�� ���ѿ�Țzj&o����}gH�5��я�i�x���*e;|#����n�pkL�����I.#Z��2As�G5����M�8���Ѓ�|��cq���M���;���U�cxˤm@����gd͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf�H��͘kCZlsf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͑)�7�u�[_��Zi�siZ͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6lٳf͛6l�]{C�W�]F�9P�x�hՔ��Q���{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#������~^��������j���{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��՛�G����Z������?/����G��5f��{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��՛�G����Z������?/����G��5f��{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��՛�G����Z������?/����G��5f��{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��՛�G����Z������?/����G��5f��{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��՛�G����Z������?/����G��5f��{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��՛�G����Z������?/����G��5f��{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��՛�G����Z������?/����G��5f��{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��՛�G����Z������?/����G��5f��{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��՛�G����Z������?/����G��5f��{�����>/��7�����t�����Y��~^��������j��#���]-?�|_�Vo�����i�#��������WKO��Վ�^��"�Q��W\O���������&'�U�������&'�U�������&'�U���A�ڋ�������A�ڋ�������A�ڋ������ ��E�I��Us�� ��G�I��Us� ��E�I��Ur�ÿ���������_���?�Q��b�\��������1?�o�������1?�W�w���_����W7�{�������W7�w���_����W/�;��j/�LO���������&'�U�������&'�U�������&'�U���A�ڋ������ ��E�I��Us� ��G�I��Us� ��G�I��Us� ��E�I��Us� ��G�I��Us�� ��G�I��Us� ��E�I��Us� ��E�I��Us�... ��A Q|H���Pw�h�q�y3͞a�<���ೳ�p�qou�Ʋ���+B�G�\}����*y\�_�)�YêL#�Eug{ �g<�I"K�����b0�|��t���Z���u��%դ�O�廘K$�6ViP�Ŭ�-��C�@�ƥQ����u{kv����,��x�g ' :���嵋yR�ǔ�� ��Ǭe7-��i�#�r��L>���\�f�M挂�]RHa��K#0*�E

People Also Search

Time Series Analysis Is A Crucial Statistical Technique Used To

Time series analysis is a crucial statistical technique used to observe data points gathered or sequenced over time. In this section, we’ll explore the foundational concepts of time series analysis, emphasizing its importance and basic methodologies. Understanding these components helps in the effective application of time series analysis in various practical scenarios, enhancing the predictive ca...

Statsmodels Is A Powerful Python Library Designed For Statistical Modeling

Statsmodels is a powerful Python library designed for statistical modeling and econometrics, particularly useful in time series analysis. This section delves into how Statsmodels can be leveraged for practical time series analysis, highlighting its compatibility and features that facilitate effective data interpretation. StatsModels is a comprehensive Python library for statistical modeling, offer...

Specifically: 1. The Function Adfuller(data['value']) Tests For The Presence Of

Specifically: 1. The function adfuller(data['value']) tests for the presence of a unit root, which would indicate non-stationarity (i.e., the mean and variance change over time). 2. The output includes an ADF test statistic and a p-value. It applies first-order differencing to the time series, which means it subtracts each value from its previous value to remove trends and stabilize the mean.

Then, It Runs The Augmented Dickey-Fuller (ADF) Test Again On

Then, it runs the Augmented Dickey-Fuller (ADF) test again on the differenced data to check if the series has become stationary (i.e., its statistical properties no longer depend on time). This is the landing page for a tutorial on time series analysis, based on Chapter 12 of Think Stats, third edition. Time series analysis provides essential tools for modeling and predicting time-dependent data, ...

Slides For The PyData Global 2024 Tutorial Are Here For

Slides for the PyData Global 2024 tutorial are here For each part of the tutorial, there are two notebook: the first contains blank cells for code-along activities and exercises; the second has all of the code and solutions to the exercises. Part 1: Introduction and Seasonal Decomposition statsmodels.tsa contains model classes and functions that are useful for time series analysis. Basic models in...