Non-seasonal Unit Root Research Articles

Re-estimation of Keynesian Model by Considering Critical Events and Multiple Cointegrating Vectors

This study employs the Mundell (1963) and Fleming (1962) traditional flow model of exchange rate to examine the long run behaviour of rupee/US $ exchange rate for Pakistan economy over the period 1982:Q1 to 2010:Q2. This study investigates the effect of output levels, interest rates and prices and different shocks on exchange rate. Hylleberg, Engle, Granger, and Yoo (HEGY) (1990) unit root test confirms the presence of non-seasonal unit root and finds no evidence of biannual and annual frequency unit root in the level of series. Johansen and Juselious (1988, 1992) likelihood ratio test indicates three long-run cointegrating vectors. Cointegrating vectors are uniquely identified by imposing structural economic restrictions on purchasing power parity (PPP), uncovered interest parity (UIP) and current account balance. Finally, the short-run dynamic error correction model is estimated on the basis of identified cointegrated vectors. The speed of adjustment coefficient indicates that 17 percent of divergence from long-run equilibrium exchange rate path is being corrected in each quarter. US war with Afghanistan has significant impact on rupee in short run because of high inflows of US aid to Pakistan after 9/11. Finally, the parsimonious short run dynamic error correction model is able to beat the naïve random walk model at out of sample forecasting horizons. JEL Classification: F31, F37, F47 Keywords: Exchange Rate Determination, Keynesian Model, Cointegration, Out of Sample Forecasting, Random Walk Model

Climate Change Prediction Using ARIMA Model

Abstract: It is a challenging task to forecast weather data accurately. The temperature change has important implications for business and economic activity. Effective management of global climate change impacts will depend upon accurate and costeffective forecasts. This paper univariate statistic techniques to model the properties of a world mean temperature dataset to develop a parsimonious forecasting model for managerial decision-making over the short-term horizon and the ARIMAbased prognostication tool has been developed by implementing the ARIMA algorithm in python. Although the model is estimated on global temperature data, the methodology could even be applied to temperature data at more localized levels. The statistical techniques include seasonal and non-seasonal unit root testing with and without structural breaks as well as ARIMA and SARIMA modelling. This paper helps us to predict the air temperature, which is the main problem of global warming. Prediction of the likely impact of climate change on monthly mean maximum and minimum temperature in Tamilnadu. Time-series techniques to develop a parsimonious model of global mean temperature change that can be used to forecast over the short-term horizon (5- 10) years. Keywords: Global warming, Forecasting, temperature

Seasonality patterns in the container shipping freight rate market

ABSTRACTShipping indexes have attracted many researchers because they reflect the overall trend of corresponding seaborne markets and can provide implications for the future. Apart from the Baltic Dry Bulk Index (BDI) and correlated indices, the China Containerized Freight Index (CCFI) has been gaining more attention. As a country with large-scale manufacturing, China is an important exporting country and the CCFI was chosen to reflect the container shipping market because the data are more convincing and representative. There have been no systematic attempts to understand the seasonality patterns of container freights. Seasonality patterns reveal the regular fluctuation patterns within a 1-year period. They exist in time series, which are observed more than once a year, like the CCFI. To investigate the nature of seasonality (stochastic and/or deterministic) in container freight rates across different line services, we analyze the CCFI. This paper uses the HEGY method and Monte Carlo method comprehensively to figure out the small sample problem. In addition, seasonal dummy variables are used to test deterministic seasonality. Except for the Japan service series, which contains a half-year unit root, the other container freight rates seem to only involve a non-seasonal unit root at the zero frequency. Deterministic seasonality exists in all the line service series. Furthermore, the seasonality depends on the balance between supply and demand. Under this premise, the seasonal law of freight rates is much obvious.

An application of a new seasonal unit root test for trending and breaking series to industrial production of the brics

Seasonality is a quite dominant source of variation in many economic time series. Several empirical studies have shown that seasonality is not a stable component but rather of stochastic nature. In this spirit, literature has seen the development of several seasonal unit root tests by generalizing the frameworks of the conventional (non-seasonal) ones. In general, existing tests for seasonal unit roots are heavily dependent on some restricted specifications for the deterministic component or they are interested in a particular observation frequency. The seasonal unit root test of [HEGY] is the most in empirical works. The strong point of this procedure is that it can distinguish between different seasonal unit roots. However, such a procedure does not take into account the breakpoints characterizing some macroeconomic data. In this study, we investigate the persistence property of the quarterly industrial production of Brazil, Russia, India, China and South Africa, covering the period of early 1990s till the last quarter of 2013, with the industrial production for BRICS characterized by strong seasonality and upward trend. For our purpose, we use the seasonal unit root test developed by , which controls for not only seasonal and trending behavior, but also for a break of unknown timing in seasonal means. Specifically, test is based on an HEGY testing strategy with innovational outliers. It has been shown that this test has a stable size even in the presence of large breaks. Also, it can accurately identify the dates of small breaks. Our results indicate that, while there exist a non-seasonal unit root in the industrial production for Brazil, India and China, there is a strong evidence a seasonal unit root at Nyquist frequency for only China. In addition, there is a strong evidence of rejection of bi-annual unit roots in all BRICS industrial production. Using coefficients for similarities, the greatest ones are recorded for Brazil and South Africa on the one hand, and Russia and South Africa on the other hand. By contrast, Russia and India have no similarity. Accordingly, some policy implications can be formulated for China as it is the only country, among the BRICS, which exhibits a seasonal unit root in its industrial production. Our results therefore, suggest that economists should examine the evolution of industrial production in China not only at the business cycle frequencies but also at the seasonal as well.

Periodic Integration and Cointegration of U.S. Stock Prices, Dividends, and Interest Rates: A New Test of the Present Value Model

This paper presents a new test of the present value model of stock price determination, using some of the recent advances in the econometrics of seasonal time series. Unlike earlier studies which generally find stock prices, dividends, and interest rates to be characterized by standard nonseasonal unit roots, we find evidence of periodic seasonal integration in these variables. This means that the conventional cointegration tests may not be robust. Using a more appropriate periodic cointegration test, our results nevertheless fail to support the present value model, thus reinforcing the case against the efficient market hypothesis.

An application of a new seasonal unit root test to inflation

In this paper, we apply the modified seasonal unit root test with seasonal level shifts at unknown time proposed by Popp (2007) to the G7 inflation rate. We also study the power properties of this test and generate critical values for a range of different break points and sample sizes. We find that there is a non-seasonal unit root in Canada's inflation rate, a semi-annual unit root in Germany's inflation rate, and no seasonal unit root at the annual frequency for any of the G7 countries.

Modelling and Forecasting Length of Stay

ABSTRACT The paper analyses, estimates and forecasts tourism demand for the region of the Sardinia (Italy). Seasonal and non-seasonal unit root tests are employed on monthly data for the sample period from 1987 to 2002. Two approaches are implemented: a quantitative analysis (i.e. a standard dynamic OLS and a SARMA with interventions) and an experts' opinion qualitative approach. A full range of diagnostic tests is provided. An ex-ante forecasting exercise is run for the period between January and December 2003 and actual data are compared with the experts' expectations and the quantitative results. Overall, evidence is provided that an integrative forecasting approach leads to more accurate forecasts.

Testing Fractional Order of Long Memory Processes: A Monte Carlo Study

Testing the fractionally integrated order of seasonal and nonseasonal unit roots is quite important for the economic and financial time series modeling. In this article, the widely used Robinson's (1994) test is applied to various well-known long memory models. Via Monte Carlo experiments, we study and compare the performances of this test using several sample sizes.

Time series modelling of global mean temperature for managerial decision-making

Climate change has important implications for business and economic activity. Effective management of climate change impacts will depend on the availability of accurate and cost-effective forecasts. This paper uses univariate time series techniques to model the properties of a global mean temperature dataset in order to develop a parsimonious forecasting model for managerial decision-making over the short-term horizon. Although the model is estimated on global temperature data, the methodology could also be applied to temperature data at more localised levels. The statistical techniques include seasonal and non-seasonal unit root testing with and without structural breaks, as well as ARIMA and GARCH modelling. A forecasting evaluation shows that the chosen model performs well against rival models. The estimation results confirm the findings of a number of previous studies, namely that global mean temperatures increased significantly throughout the 20th century. The use of GARCH modelling also shows the presence of volatility clustering in the temperature data, and a positive association between volatility and global mean temperature.

THE BEHAVIOR OF HEGY TESTS FOR QUARTERLY TIME SERIES WITH SEASONAL MEAN SHIFTS

ABSTRACT This paper studies the behavior of the HEGY statistics for quarterly data, for seasonal autoregressive unit roots, when the analyzed time series is deterministic seasonal stationary but exhibits a change in the seasonal pattern. We analyze also the HEGY test for the nonseasonal unit root. the data generation process being trend stationary too. Our results show that when the break magnitudes are finite, the HEGY test statistics are not asymptotically biased toward the nonrejection of the seasonal and nonseasonal unit root hypotheses. However, the finite sample power properties may be substantially affected, the behavior of the tests depending on the type of the break.

Seasonality Tests

This article modifies and extends the test against nonstationary stochastic seasonality proposed by Canova and Hansen. A simplified form of the test statistic in which the nonparametric correction for serial correlation is based on estimates of the spectrum at the seasonal frequencies is considered and shown to have the same asymptotic distribution as the original formulation. Under the null hypothesis, the distribution of the seasonality test statistics is not affected by the inclusion of trends, even when modified to allow for structural breaks, or by the inclusion of regressors with nonseasonal unit roots. A parametric version of the test is proposed, and its performance is compared with that of the nonparametric test using Monte Carlo experiments. A test that allows for breaks in the seasonal pattern is then derived. It is shown that its asymptotic distribution is independent of the break point, and its use is illustrated with a series on U.K. marriages. A general test against any form of permanent seasonality, deterministic or stochastic, is suggested and compared with a Wald test for the significance of fixed seasonal dummies. It is noted that tests constructed in a similar way can be used to detect trading-day effects. An appealing feature of the proposed test statistics is that under the null hypothesis, they all have asymptotic distributions belonging to the Cramér–von Mises family.

Consumer Bankruptcies and the Bankruptcy Reform Act: A Time-Series Intervention Analysis, 1960–1997

The Bankruptcy Reform Act of 1978, effective on October 1, 1979, significantly altered the basic rules by which consumers file for bankruptcy. Between 1979 and 1997, the number of nonbusiness bankruptcies filed annually rose from 200,000 to 1.35 million, and the rate of bankruptcies per 100,000 adults increased from 129 to 715. A controversial aspect of bankruptcy is how much of this increase can be attributed to the 1978 act. Early empirical studies provide estimates ranging from a low of 6% to a high of 75% for the immediate post-act period. However, two recent studies using longer data series report that none of the increase was due to the act. Previous studies suffer from several econometric problems, including inadequate attention to stochastic properties and stationarity of the data series, as well as data errors due to reporting changes. This paper uses an ARIMA intervention analysis to estimate the impact of the 1978 act. Using adjusted quarterly data for 1960:3 to 1995:4, the data first are examined for unit roots. The tests reject the presence of seasonal unit roots but confirm the presence of a nonseasonal unit root. The empirical analysis therefore is based on logged first differences of bankruptcy filings and filing rates per capita. An ARIMA model is estimated using the preintervention data for 1960:3 to 1979:3. This model is re-estimated for 1960:3 to 1995:4 with the intervention terms included. The intervention model estimates indicate that the 1978 act increased consumer bankruptcies by 36% in the post-act period relative to the pre-act period, or about 72,400 additional bankruptcies per year. Overall, the net impact of the 1978 act was modest compared to the substantial rise in bankruptcies that has occurred since 1979.

On the Role of Seasonal Intercepts in Seasonal Cointegration

In the paper we consider the role of seasonal intercepts in seasonal cointegration analysis. For the nonseasonal unit root, such intercepts can generate a stochastic trend with a drift common to all observations. For the seasonal unit roots, however, we show that unrestricted seasonal intercepts generate trends that are different across the seasons. Since such seasonal trends may not appear in economic data, we propose a modified empirical method to test for seasonal cointegration. We evaluate our method using Monte Carlo simulations and using a four‐dimensional data set of Austrian macroeconomic variables.

Critical values for unit root tests in seasonal time series

Summary In this paper, we present tables with critical values for a variety of tests for seasonal and non-seasonal unit roots in seasonal time series. We consider (extensions of) the Hylleberg et al. and Osborn et al. test procedures. These extensions concern time series with increasing seasonal variation and time series with structural breaks in the seasonal means. For each case, we give the appropriate auxiliary test regression, the test statistics, and the corresponding critical values for a selected set of sample sizes. We also illustrate the practical use of the auxiliary regressions for quarterly new car sales in the Netherlands. Supplementary to this paper, we provide Gauss programs with which one can generate critical values for particular seasonal frequencies and sample sizes.

Periodic integration: further results on model selection and forecasting

This paper considers model selection and forecasting issues in two closely related models for nonstationary periodic autoregressive time series [PAR]. Periodically integrated seasonal time series [PIAR] need a periodic differencing filter to remove the stochastic trend. On the other hand, when the nonperiodic first order differencing filter can be applied, one can have a periodic model with a nonseasonal unit root [PARI]. In this paper, we discuss and evaluate two testing strategies to select between these two models. Furthermore, we compare the relative forecasting performance of each model using Monte Carlo simulations and some U.K. macroeconomic seasonal time series. One result is that forecasting with PARI models while the data generating process is a PIAR process seems to be worse thanvice versa.

Modelling the Seasonal Patterns in UK Macroeconomic Time Series

SUMMARY This paper examines the seasonal patterns and comovements of quarterly UK macroeconomic time series. The framework used to analyse seasonal fluctuations enables both deterministic and stochastic seasonal factors to be modelled, with these factors being estimated by signal extraction. Tests for both factors are performed and it is found that, although both forms of seasonality are usually present, seasonality is much smaller in prices and interest rates than in output and its components. It is also found that the majority of series contain both seasonal and non-seasonal unit roots, but that there is no evidence of cointegration at either the zero or seasonal frequencies between output and consumption and between output or prices and money.

Seasonal unit-root tests on Canadian macroeconomic time series

In this note we subject some Canadian macroeconomic time series to test of seasonal and non-seasonal unit roots. Overall we find evidence that the series are integrated at some of the seasonal frequencies as at a zero frequency.