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Lecture 2 Stephen G Hall Time Series Forecasting

Introduction. These are a body of techniques which rely primarily on the statistical properties of the data, either in isolated single series or in groups of series, and do not exploit our understanding of the working of the economy at all. . . The objective is not to build models which are a good representation of the economy with all its complex interconnections, but rather to build simple models which capture the time series behaviour of the data and may be used to provide an adequate basis f33171

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Lecture 2 Stephen G Hall Time Series Forecasting

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    1. Lecture 2 Stephen G Hall Time Series Forecasting

    2. Introduction These are a body of techniques which rely primarily on the statistical properties of the data, either in isolated single series or in groups of series, and do not exploit our understanding of the working of the economy at all.

    3. The objective is not to build models which are a good representation of the economy with all its complex interconnections, but rather to build simple models which capture the time series behaviour of the data and may be used to provide an adequate basis for forecasting alone.

    4. See `Applied Economic Forecasting Techniques' ed S G Hall, Simon and Schuster, 1994.

    5. Some basic concepts Two basic types of time series models exist, these are autoregressive and moving average models.

    9. ARMA models A mixture of these two types of model would be referred to as an autoregressive moving average model (ARMA)n,q, where n is the order of the autoregressive part and q is the order of the moving average term.

    12. The Correlogram and partial autocorellation function Two important tools for diagnosing the time series properties of a series

    15. Stationarity

    20. `Ad Hoc' forecasting procedures a broadly sensible approach to forecasting but they are not the result of a particular economic or statistical view about the way the data was generated.  

    26. The Box-Jenkins approach Box and Jenkins (1976) proposed a modelling strategy for pure time series forecasting The Box-Jenkins procedure may be seen as one of the early attempts to confront the problem of non-stationary data. The Box Jenkins modelling procedure consists of three stages; identification, estimation and diagnostic checking.

    27. At the identification stage a set of tools are provided to help identify a possible ARIMA model, which may be an adequate description of the data.   Estimation is simply the process of estimating this model.   Diagnostic checking is the process of checking the adequacy of this model against a range of criteria and possibly returning to the identification stage to respecify the model.   The distinguishing stage of this methodology is identification.

    28. This approach tries to identify an appropriate ARIMA specification. It is not generally possible to specify a high order ARIMA model and then proceed to simplify it as such a model will not be identified and so can not be estimated. The first stage of the identification process is to determine the order of differencing which is needed to produce a stationary data series. The next stage of the identification process is to assess the appropriate ARMA specification of the stationary series.

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