Time Series Assignment Essay Example | Topics and Well Written Essays - 1500 words

Time Series Assignment - Essay Example Autocorrelation function (ACF) is the  cross-correlation  of a  signal  with itself. It refers to the similarity between observations as a function of the time lag between them. ACF is a statistical tool for finding repeating patterns, for example the presence of a periodic signal obscured by noise, or may be identifying the  missing fundamental frequency (Box and Jenkins, 1994) in a signal implied by its  harmonic  frequencies.   Just like ACF, PACF plots (Box and Jenkins, 2008) are also commonly used tool for identifying the order of an  autoregressive model. The partial autocorrelation of an AR (p) process is zero at lag  p  +  1 and greater. If the sample autocorrelation plot indicates that an AR model may be appropriate, then the sample partial autocorrelation plot is examined to help identify the order. One looks for the point on the plot where the partial autocorrelations for all higher lags are essentially zero. Placing on the plot an indication of the sampling uncertainty of the sample PACF is helpful for this purpose: this is usually constructed on the basis that the true value of the PACF, at any given positive lag, is zero. If the PACF displays a sharp cut-off while the ACF decays more slowly (i.e., has significant spikes at higher lags), we say that the stationarized series displays an "AR signature," meaning that the autocorrelation pattern can be explained more easily by adding AR terms rather than by adding MA terms. The plots clearly displays a sharp cut-off for the PACF and a significantly reducing value of spikes for the ACF implying that we instead use an AR