## Periodicity and Stochastic Trends in Economic Time SeriesThis book provides a self-contained account of periodic models for seasonally observed economic time series with stochastic trends. Two key concepts are periodic integration and periodic cointegration. Periodic integration implies that a seasonally varying differencing filter is required to remove a stochastic trend. Periodic cointegration amounts to allowing cointegration paort-term adjustment parameters to vary with the season. The emphasis is on useful econrameters and shometric models that explicitly describe seasonal variation and can reasonably be interpreted in terms of economic behaviour. The analysis considers econometric theory, Monte Carlo simulation, and forecasting, and it is illustrated with numerous empirical time series. A key feature of the proposed models is that changing seasonal fluctuations depend on the trend and business cycle fluctuations. In the case of such dependence, it is shown that seasonal adjustment leads to inappropriate results. |

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### Contents

An introduction to seasonal time series | 32 |

Seasonal adjustment | 49 |

Seasonal integration and cointegration | 61 |

Copyright | |

6 other sections not shown

### Other editions - View all

Periodicity and Stochastic Trends in Economic Time Series Philip Hans Franses No preview available - 1996 |

### Common terms and phrases

A4 filter A4yt analysis autocovariance auxiliary regression Box-Jenkins business cycle cent level Chapter characteristic equation cointegration relations consider constant consumption correlation corresponds CRDF critical values denoted diagnostic differencing filter dummy variables eigenvalues empirical example F-test forecasts fractiles Ghysels given HEGY Hence Hylleberg indicate industrial production Johansen lags linear matrix Monte Carlo moving average nondurables nonperiodic models nonseasonal components nonseasonal unit root null hypothesis parameters partial autocorrelations periodic autoregression periodic integration periodic models periodic time series PIAR model PIAR process polynomial process yt quarter quarterly real GNP rejection frequencies results in Table sample series SARIMA SARIMA models seasonal adjustment seasonal and nonseasonal seasonal cointegration seasonal component seasonal fluctuations seasonal patterns seasonal time series seasonal unit roots seasonal variation Section series models series yt significance simulation stationary stochastic trend test statistics tion UK total unemployment univariate univariate time series vector process Wald test white noise yt series zero