Abstract
Time series analysis of Nigerian Unemployment Rates is done. The data used is monthly from 1948 to 2008. The time plot reveals a slightly positive trend with no clear seasonality. A multiplicative seasonal model is suggestive given seasonality that typically tends to increase with time. Seasonal differencing once produced a series with no trend nor discernible stationarity. A non-seasonal differencing of the seasonal differences yielded a series with no trend but with a correlogram revealing stationarity of order 12, a nonseasonal autoregressive component of order 3 and a seasonal moving average component of order 1. A multiplicative seasonal autoregressive integrated moving average (ARIMA) model, (3, 1, 0)x(0, 1, 1)12, is fitted to the series. It has been shown to be adequate.
Highlights
A time series is defined as a set of data collected sequentially in time
The autocorrelation is a function of the lag separating the correlated values and called the autocorrelation function (ACF)
An AR(p) model may be defined as a model whereby a current value of the time series Xt depends on the immediate past p values: Xt-1, Xt-2, ... , Xt-p
Summary
A time series is defined as a set of data collected sequentially in time. It has the property that neighbouring values are correlated. On the other hand an MA(q) model is such that the current value Xt is a linear combination of immediate past values of the white noise process: Apart from stationarity, invertibility is another important requirement for a time series. It refers to the property whereby the covariance structure of the series is unique (Priestley, 1981). Differencing to degree d renders the series stationary.The model (3) is said to be an autoregressive integrated moving average model of orders p, d and q and designated ARIMA(p, d, q)
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