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36) The above is an ARMA (p, q) process, autoregression of order p and moving average of order q. The family of univariate time series models are not complete without a third element, orders of integration. Recall one of the requirements for regression analysis is that the data to be analysed must be stationary. A time series may or may not be stationary. Taking difference operations usually can make a nonstationary time series become stationary. When a time series requires d times of differencing to become stationary, it is said to be integrated of order d, designated I (d).

It is a combination of two previously learned distributions, the normal distribution and the χ 2 -distribution. 18) The random variable of the above kind is said to obey a t-distribution with T degrees of freedom. 8 t-distributions with different degrees of freedom. When degrees of freedom become infinite, a t-distribution approaches a normal distribution. Now let us consider the need in estimation of the accuracy of an estimate. 9). 22) measures the ‘meaningfulness’ of b, or the closeness of b to β.

If a time series needs the difference operation once to achieve stationarity, it is an I (1) series; and a time series is I (n) if it is to be differenced for n times to achieve stationarity. An I (0) time series has no roots on or inside the unit circle but an I (1) or higher-order integrated time series contains roots on or inside the unit circle. So, examining stationarity is equivalent to testing for the existence of unit roots in the time series. 1) where μ is a constant or drift, which can be zero, in the random walk.

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