Seasonal Time Series Models Research Articles

Testing for Nonstationary Parameter Specifications in Seasonal Time Series Models

Let $Y_t$ be an autoregressive process satisfying $Y_t = \alpha_1 Y_{t - 1} + \alpha_2 Y_{t - d} + \alpha_3 Y_{t - d - 1} + e_t$, where $\{e_t\}^\infty_{t = 0}$ is a sequence of $\operatorname{iid}(0, \sigma^2)$ random variables and $d \geq 2$. Such processes have been used as parametric models for seasonal time series. Typical values of $d$ are 2, 4, and 12 corresponding to time series observed semi-annually, quarterly, and monthly, respectively. If $\alpha_1 = 1, \alpha_2 = 1, \alpha_3 = - 1$ then $\Delta_1\Delta_d Y_t = e_t$, where $\Delta_r Y_t$ denotes $Y_t - Y_{t - r}$. If $(\alpha_1, \alpha_2, \alpha_3) = (1, 1, - 1)$ the process is nonstationary and the theory for stationary autoregressive processes does not apply. A methodology for testing the hypothesis $(\alpha_1, \alpha_2, \alpha_3) = (1, 1, - 1)$ is presented and percentiles for test statistics are obtained. Extensions are presented for multiplicative processes, for higher order processes, and for processes containing deterministic trend and seasonal components.

Analysis of Economic Time Series.

Analysis of Economic Time Series: A Synthesis integrates several topics in economic time-series analysis, including the formulation and estimation of distributed-lag models of dynamic economic behavior; the application of spectral analysis in the study of the behavior of economic time series; and unobserved-components models for economic time series and the closely related problem of seasonal adjustment. Comprised of 14 chapters, this volume begins with a historical background on the use of unobserved components in the analysis of economic time series, followed by an Introduction to the theory of stationary time series. Subsequent chapters focus on the spectral representation and its estimation; formulation of distributed-lag models; elements of the theory of prediction and extraction; and formulation of unobserved-components models and canonical forms. Seasonal adjustment techniques and multivariate mixed moving-average autoregressive time-series models are also considered. Finally, a time-series model of the U.S. cattle industry is presented. This monograph will be of value to mathematicians, economists, and those interested in economic theory, econometrics, and mathematical economics.

Interpreting Partial Autocorrelation Functions of Seasonal Time Series Models

Interpreting Partial Autocorrelation Functions of Seasonal Time Series Models

On the Strong Mixing Property for Linear Sequences

On the Strong Mixing Property for Linear Sequences

Interpreting partial autocorrelation functions of seasonal time series models

Interpreting partial autocorrelation functions of seasonal time series models