Cointegration Springer

Leo Migdal

-Dec 14, 2025, 4:32 AM

Part of the book series: Palgrave Texts in Econometrics ((PTEC)) In this chapter the case where there are a number of non-stationary series driven by common processes is considered. It was shown in the previous chapter that the underlying behaviour of time series may follow from a range of different time series processes. Time series models separate into autoregressive processes that have long-term dependence on past values and moving average (MA) processes that are dynamic but limited in terms of the way they project back in time. In the previous chapter the issue of non-stationarity was addressed in a way that was predominantly autoregressive, that is stationarity testing via the comparison of a difference stationary process under the null with a... The technique is extended to consider the extent to which the behaviour of the discrepancy between two series is stationary or not.

In the context of single equations, a Dickey-Fuller test can be used to determine whether such series are related, and when they are this is called cointegration. When it comes to analysing more than one series then the nature of the time series process driving the data becomes more complicated and the number of combinations of non-stationary series that are feasible... This is a preview of subscription content, log in via an institution to check access. Tax calculation will be finalised at checkout Without explaining or deriving the origin of the vector for the white noise process, this equality is best interpreted as meaning the autocorrelation structure of the processes on each side of the equation are... All material on this site has been provided by the respective publishers and authors.

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The concept of co-integration posits that the linear combination of two or more nonstationary time series can be stationary if they are co-integrated (Granger 1981). Co-integration and error correction models are largely applied to solve the spurious regression problem resulting from the inclusion of nonstationary variables in a regression model. Two main approaches to modeling co-integration are single-equation residual-based and system-based analyses. One precondition for the above tests is that all variables in the co-integration regression should be integrated with the same order. When different orders of integration are identified, alternative tests such as the autoregressive distributed lag bounds test can be applied (Pesaran et al. 2001).

Since the mid-1990s, a considerable number of tourism researchers have adopted the co-integration method to address a variety of topics related to tourism demand modeling and forecasting. Numerous efforts have been undertaken to empirically... This is a preview of subscription content, log in via an institution to check access. Tax calculation will be finalised at checkout Corresponding author chengyitu@berkeley.edu Received 2019 May 19; Revised 2019 Jul 22; Accepted 2019 Aug 25; Collection date 2019 Sep 27.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Cointegration focuses on whether the long-term linear relationship between two or more time series is stationary even if this linear relationship does not exist or is not strong for the short term. Identifying the potential cointegration is important for economics, ecology, meteorology, neuroscience, and much more. Classic methods only considered or restricted in cointegration where the order of integration of all time series is 1. We introduce a method based on searching the vector to minimize the absolute correlation of convergent cross-mapping that can explore the universal cointegration and its extent. The proposed method can be applied to time series whose order of integration is not 1, cases that are not covered by classic cointegration.

The proposed method is first illustrated and validated through time series generated by mathematical models in which the underlying relationships are known and then applied to three real-world examples. Subject Areas: Global Change, Interdisciplinary Physics, Computational Mathematics A Correction to this article was published on 27 December 2021 There is a growing literature documenting that the persistence of time series may change over time, and as a consequence, shifts in the long-run equilibrium of macroeconomic variables are expected. An important example is the significant increase in public debt in certain periods of time due to increases in government expenditures which are not matched by revenue counterparts. In this paper, new residual-based Wald-type tests are proposed which are designed to detect segmented cointegration, i.e., subsamples during which equilibrium relations exist.

We derive the asymptotic properties of the tests, tabulate critical values for models with different deterministic components, and show by simulations that the tests display good finite sample performance in many relevant setups. Our empirical application provides a thorough examination of the main components of US governments’ budgets at two administrative levels (Federal, and State and Local) and concludes that until Bill Clinton’s presidency government budgets components... This is a preview of subscription content, log in via an institution to check access. Price excludes VAT (USA) Tax calculation will be finalised during checkout. A Correction to this paper has been published: https://doi.org/10.1007/s00181-021-02187-0 All material on this site has been provided by the respective publishers and authors.

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Cointegration Springer

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