Difference Stationary Processes Research Articles

Forecasting of Male Life Expectancy in Nigeria: Box-Jenkins Approach

Over the past few decades, Males’ life expectancy has been observed to be less than that of females. In the literature, little has been done to forecast the Life expectancy at birth for Males (LEM) in developing countries, especially in Nigeria. To understand the forecasting dynamics of LEM in Nigeria, this work therefore examines the series using the Box-Jenkins (1976) methodology. Pre-examination tests conducted on the series revealed that it is not only a difference stationary process of order one {I(1)} but it is also best fitted by ARIMA (1, 1, 1) model. Moreover, diagnostic checking carried out on the residuals of the fitted model confirmed that the residual is a white noise error term in that it fulfils the assumptions of homoscedasticity, stationarity, and autocorrelation. To obtain a good forecast, the LEM data spanning 1960 to 2014 (55 years) were used to train the model while the remaining LEM data spanning 2015 to 2020 (6 years) were used to test the data. For the test data, the forecasted LEM has been shown to give approximate values of the actual LEM. Findings showed that the LEM is expected to increase slightly by 0.64% within the forecasted periods spanning 2021 to 2030. Diagnostic checking, Forecasting, Homoscedasticity, Life expectancy, Male, Training sets, Testing sets

Agriculture Financing for Output Growth: A Focus on Livestock Production in Nigeria

In this study, the effect of agriculture financing such as the agricultural credit guarantee scheme fund, bank loans and advances to agriculture, and foreign aid to agriculture on livestock production was examined in Nigeria from 1981 to 2021. Annual time series data for each of the variables were obtained from the Central Bank of Nigeria (CBN) Statistical Bulletin and the Organisation for Economic Cooperation and Development (OECD) Statistics. The method of data analysis includes descriptive statistics, a parsimonious error correction model (ECM), and diagnostic tests. Evidence of the first difference stationary processes was established from the unit root test results. This indicates that the variables are all integrated of order one, I(1). The Johansen cointegration test results show that the variables in the model have a long-run relationship. The parsimonious ECM shows that the agriculture credit guarantee scheme fund has a positive and significant effect on livestock output. The estimated parameters show that a 1% increase in the current value of the agriculture credit guarantee scheme fund leads to a 0.0244% increase in livestock output. Similarly, it was found that livestock output increased by 0.0183% following a 1% increase in the first-lag agriculture credit guarantee scheme fund. The findings highlight the importance of agriculture financing in boosting the growth of livestock production in Nigeria. The results further show that bank loans and advances, as well as foreign aid to agriculture, negatively and significantly affected livestock production. The error correction coefficient (-0.297) is negative and significant at the 5% level.

COVID-19 and domestic trade in Bulgaria

Domestic trade is an essential contributor to economic growth and an indicator of the people’s welfare. It is vulnerable to the COVID-19 crisis due to the pandemic itself and the government’s measures against it. An accurate estimation of the pandemic influence on domestic trade is needed for effective economic intervention in support of the economic recovery and improvement of the well-being of the population. The aim of this paper is to estimate the magnitude and timing of the COVID-19 impact on domestic trade in Bulgaria. The data used in the study covered the period 2000–2020 with monthly data for the indicator “Turnover for wholesale and retail trade and repair of motor vehicles and motorcycles in Bulgaria.” This paper employed unit root tests, autocorrelation function analysis, building, estimating, forecasting ARIMA and ARCH models, and intervention analysis. The results revealed that Bulgarian domestic trade followed the difference-stationary process as unit root tests failed to reject the random walk hypothesis. The COVID-19 impact on domestic trade proved to be long-lasting and has permanently decreased its level since March 2020. The timing of the impact coincided with the government’s measures against the pandemic. The drop in the volume of domestic trade was substantial and estimated at 19.3%. Following the nature of domestic trade, determined and decisive intervention is necessary if the Bulgarian government seeks to expand domestic demand and successfully procure economic recovery.

Unit roots in real primary commodity prices? A meta-analysis of the Grilli and Yang data set

The long-run behavior of real primary commodity prices, especially whether these series are trend stationary or contain a unit root, has been a topic of major debate in applied economics. In this paper, I perform a meta-analysis and combine the evidence of 12 representative studies on the subject in order to reach a unified conclusion about the presence of unit roots in these prices. The studies use different testing procedures, but share the common null hypothesis of a difference stationary process. Also, they use the individual price indices from the Grilli and Yang data set that is arguably one the most popular sources of long-term data on commodity prices. The combined evidence against unit roots in real primary commodity prices is strong: out of 24 cases, the unit root is not rejected in at most four. This rate means that real primary commodity prices are mean reverting and thus, to some degree, forecastable.

Detecting stock market turning points using wavelet leaders method

Detecting stock market turning points is a task with great significance and challenges. To achieve this purpose, we decompose the trend and cycle components of stock prices by the autoregressive fractionally integrated moving average model, which can simulate fractional difference stationary processes. What is more, we use wavelet leaders method to analyze multifractal characteristics of the cycle component and then propose two new indicators to detect the market turning points. Empirically, both indicators perform very well in detecting all critical turning points of US and China stock markets. Most importantly, compared with Bai et al. (2015) by testing the same data, our method detects turning points more accurately.

Spurious OLS Estimators of Detrending Method by Adding a Linear Trend in Difference-Stationary Processes—A Mathematical Proof and Its Verification by Simulation

Adding a linear trend in regressions is a frequent detrending method in economic literatures. The traditional literatures pointed out that if the variable considered is a difference-stationary process, then it will artificially create pseudo-periodicity in the residuals. In this paper, we further show that the real problem might be more serious. As the Ordinary Least Squares (OLS) estimators themselves are of such a detrending method is spurious. The first part provides a mathematical proof with Chebyshev’s inequality and Sims–Stock–Watson’s algorithm to show that the OLS estimator of trend converges toward zero in probability, and the other OLS estimator diverges when the sample size tends to infinity. The second part designs Monte Carlo simulations with a sample size of 1,000,000 as an approximation of infinity. The seed values used are the true random numbers generated by a hardware random number generator in order to avoid the pseudo-randomness of random numbers given by software. This paper repeats the experiment 100 times, and gets consistent results with mathematical proof. The last part provides a brief discussion of detrending strategies.

TREND-CYCLE DECOMPOSITIONS OF REAL GDP REVISITED: CLASSICAL AND BAYESIAN PERSPECTIVES ON AN UNSOLVED PUZZLE

While Perron and Wada (2009) maximum likelihood estimation approach suggests that postwar US real GDP follows a trend stationary process (TSP), our Bayesian approach based on the same model and the same sample suggests that it follows a difference stationary process (DSP). We first show that the results based on the approach should be interpreted with caution, as they are relatively more subject to the ‘pile-up problem’ than those based on the Bayesian approach. We then directly estimate and compare the two competing TSP and DSP models of real GDP within the Bayesian framework. Our empirical results suggest that a DSP model is preferred to a TSP model both in terms of in-sample fits and out-of-sample forecasts.

Discrimination between trend and difference stationary processes based on adaptive lasso

Discrimination between trend and difference stationary processes based on adaptive lasso

On Singular Spectrum Analysis And Stepwise Time Series Reconstruction

This article provides a detailed statistical analysis of a new approach to singular spectrum analysis (SSA). It examines SSA constructed using re‐scaled trajectories (RT‐SSA) and presents a theoretical analysis of RT‐SSA under very general conditions concerning the structure of the observed series. The spectral features of population ensemble models implicit in the large sample properties of RT‐SSA are investigated, motivating a new time series modelling methodology based on a stepwise application of RT‐SSA. The operation of the theoretical results is illustrated via numerical examples involving trend stationary and difference stationary processes, and a random walk with drift. An analysis of the S&P 500 index also serves as a vehicle to demonstrate the practical impact of the stepwise RT‐SSA processing methodology.

Trend-Cycle Decompositions of Real GDP Revisited: Classical and Bayesian Perspectives on an Unsolved Puzzle

While Perron and Wada (2009) show that postwar U.S. real GDP follows a trend stationary process (TSP) based on the maximum likelihood approach, our analysis based on the Bayesian approach shows that it is a difference stationary process (DSP) with the stochastic trend component explaining most of the variations in real GDP. One goal of this paper is to provide a comprehensive analysis on the sources of such different results and to suggest that more credibility should be conferred to the Bayesian inference. Another goal naturally is to re-investigate the trend-cycle decompositions within the Bayesian framework. This is done by employing a model that incorporates time variation in both the mean and variance. The Bayesian approach to model selection prefers a DSP model to a TSP model, even though the evidence is less than decisive. Empirical results also show that there exists convincing evidence that the cycle from the DSP model, which is small in magnitude and noisy, has out-of-sample predictive power for future output growth at short horizons. The highly persistent TSP cycle without any predictive power may be related to spurious periodicity discussed in Nelson and Kang (1981).

Are real GDP levels nonstationary across Central and Eastern European countries?

This study applies the Sequential Panel Selection Method (SPSM) proposed by Chortareas and Kapetanios (2009) to investigate and assess the non-stationary properties of whether real GDP follows a trend stationary or a difference stationary process for Central Eastern European (CEE) countries. SPSM can classify the whole panel into a group of stationary series and a group of non-stationary series. We clearly identify how many and which series in the panel are stationary processes and provide robust evidence clearly indicating that per capita real GDP for CEE countries holds stationary for three countries. Our findings point out their per capita real GDP convergence is a mean reversion towards equilibrium values in a non-linear way. Our results have important policy implications for macroeconomic policy, modeling, testing and forecasting for these CEE countries under study.

Characterising economic trends by Bayesian stochastic model specification search

A recently proposed Bayesian model selection technique, stochastic model specification search, is carried out to discriminate between two trend generation hypotheses. The first is the trend-stationary hypothesis, for which the trend is a deterministic function of time and the short run dynamics are represented by a stationary autoregressive process. The second is the difference-stationary hypothesis, according to which the trend results from the cumulation of the effects of random disturbances. A difference-stationary process may originate in two ways: from an unobserved components process adding up an integrated trend and an orthogonal transitory component, or implicitly from an autoregressive process with roots on the unit circle. The different trend generation hypotheses are nested within an encompassing linear state space model. After a reparameterisation in non-centred form, the empirical evidence supporting a particular hypothesis is obtained by performing variable selection on the model components, using a suitably designed Gibbs sampling scheme. The methodology is illustrated with reference to a set of US macroeconomic time series which includes the traditional Nelson and Plosser dataset. The conclusion is that most series are better represented by autoregressive models with time-invariant intercept and slope and coefficients that are close to boundary of the stationarity region. The posterior distribution of the autoregressive parameters provides useful insight on quasi-integrated nature of the specifications selected.

Yule's lambdagram revisited and reclaimed

In this article, the lambdagram, proposed by Yule in his last time series paper published in 1945, is revisited using modern theoretical and computational developments unavailable to him. Although it is not particularly good at identifying stationary processes, the lambdagram is found to be much more useful for distinguishing between trend and difference stationary processes. The lambdagram is applied to the Nelson–Plosser data and the conclusions drawn from using it are compared with other analyses of this data set.

Estimation of fractional integration under temporal aggregation

A result characterizing the effect of temporal aggregation in the frequency domain is known for arbitrary stationary processes and generalized for difference-stationary processes here. Temporal aggregation includes cumulation of flow variables as well as systematic (or skip) sampling of stock variables. Next, the aggregation result is applied to fractionally integrated processes. In particular, it is investigated whether typical frequency domain assumptions made for semiparametric estimation and inference are closed with respect to aggregation. With these findings it is spelled out, which estimators remain valid upon aggregation under which conditions on bandwidth selection.

Direct and iterated multistep AR methods for difference stationary processes

The paper focuses on the comparison of the direct and iterated AR predictors when Xt is a difference stationary process. In particular, it provides some useful results for comparing the efficiency of the two predictors and for extracting the trend from macroeconomic time series using the two methods. The main results are based on an encompassing representation for the two predictors which enables to derive their properties quite easily under a maintained model. The paper provides an analytic expression for the mean square forecast error of the two predictors and derives useful recursive formulae for computing the direct and iterated coefficients. From the empirical standpoint, we propose estimators of the AR coefficients based on the tapered Yule-Walker estimates; we also provide a test of equal forecast accuracy which is very simple to implement and whose critical values can be obtained with the bootstrap method. Since multistep prediction is tightly bound up with the estimation of the long run component in a time series, we turn to the role of the direct method for trend estimation and derive the corresponding multistep Beveridge-Nelson decomposition.

Trends of U.S. Emissions of Nitrogen Oxides and Volatile Organic Compounds

Time-series analysis of how government regulation has affected the U.S. air pollution trends since 1970 has generated considerable interest in the area of environmental economics . Using recently developed structural break tests that are valid for difference-stationary (DS) and trendstationary (TS) data and efficient unit root tests that allow for breaks we examine the trend behavior of two air pollutants, Nitrogen Oxides (NOX) and Volatile Organic Compounds (VOC). We concentrate on answering two questions. First, was there a break in the trends of NOX and VOCs emissions around the time the CAAA of 1970 were passed? And second, are the U.S. emissions of NOX and VOC trend-stationary or difference-stationary. Existence of a reduction in the slope of the trend in pollution emissions around the timing of the CAAA of 1970 provides strong evidence of the effectiveness of the policy, and the distinction between DS and TS processes is important for assessing the potential long-term impact of environmental policy which relies on forecasting future emissions and evaluating the accuracy of these forecasts. We find that there was a break in the trend of both air pollutants at the time the Clean Air Act Amendments of 1970 were passed. The unit root tests show that NOX are difference-stationary

Output fluctuations: transitory or permanent? the case of Latin America

This article investigates the time series properties of per capita real output for 19 Latin American Countries over the period 1965 to 2004. This empirical study examines the significance of contemporaneous correlations among cross sectional residuals using two newly developed tests. The tests find evidence of cross sectional dependence and induce us to use the SURADF and the CADF panel unit root tests, which allow for cross sectional dependence. The tests indicate that the real output in Latin American countries are characterized by a difference stationary process and output fluctuations seem to be permanent. These findings have important policy implications for these countries.

Correlation analysis and causality test between Ludong-Huanghai block and South Japan

In this paper, we make a comparative analysis and correlation test for the seismic activities in the South Japan and the Ludong-Huanghai block (a secondary tectonic unit in the North China) and approach the relationship between the energy release processes of these two areas by using co-integration analysis and Granger causality test for the time series of random variables. The results show that the seismic activities in these two areas are correlative and synchronous to a certain extent, and their release series of cumulative strain energy are contemporaneously correlative. Both energy series are first-order difference stationary processes and there is secular and steady co-integration between them. We make a positive analysis on the first-order difference energy series through Granger causality test based on vector error correction (VEC) model and find there is unilateral Granger causality and prominent co-integration between the two energy release processes.

Time Series Properties of Capitalization Rates: A Comment and Extension

Abstract No abstract available.

Methods of Analyzing the Nonstationary Time Series with Implicit Changes in Their Properties

The problems of analysis of the nonstationary time series with explicit and implicit changes in their properties were discussed. The main approaches and methods of analysis of the nonstationary processes were described. Consideration was given to the trend-stationary and difference-stationary processes. The algorithms to determine the process type hinge on verifying hypotheses like "initial process is a DS-process (TS-process)" against the alternative ones. The notions of false regression and cointegration were discussed. The problems arising at analysis of the varying-property processes and methods of their solution were reviewed. Consideration was given to the cases of explicit and implicit changes and algorithms of detection in the current and a posteriori modes.