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

Time Series Assignment - Essay ExampleAutocorrelation function (ACF) is thecross-correlationof asignalwith itself. It refers to the similarity in the midst of 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 semestral signal obscured by noise, or may be identifying themissing fundamental frequency (Box and Jenkins, 1994) in a signal implied by itsharmonicfrequencies.Just like ACF, PACF plats (Box and Jenkins, 2008) are also commonly used tool for identifying the order of anautoregressive model. The partial autocorrelation of an AR (p) process is zero at lagp+1 and greater. If the hear 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(prenominal) lags are essentially zero. Placing on the plot an indi cation 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