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A discrete-TIme signal or TIme series [1] is a set ofobservaTIons taken sequenTIally in time, space or some otherindependent variable. Many sets of data appear as time series:a monthly sequence of the quantity of goods shipped from afactory, a weekly series of the number of road accidents,hourly observations made on the yield of a chemical processand so on. Examples of time series abound in such fields aseconomics, business, engineering, natural sciences, medicineand social sciences.An intrinsic feature of a time series is that, typically,adjacent observations are related or dependent. The nature ofthis dependence among observations of a time series is ofconsiderable practical interest. Time Series Analysis isconcerned with techniques for the analysis of this dependence[2]. This requires the development of models for time seriesdata and the use of such models in important areas ofapplication.A discrete-time signal x (n) is basically a sequence of realor complex numbers called samples. Discrete-time signals canarise in various ways. Very often, a discrete-time signal isobtained by periodically sampling a continuous-time signal,that is x (n) = xc (nT), where T = 1 / Fs is the sampling periodand Fs is the sampling frequency. At other times, the samplesof a discrete-time signal are obtained by accumulating somequantity over equal intervals of time, for example, the numberof cars per day traveling on a certain road. Financial signals,like daily stock market prices are inherently discrete-time.When successive observations of the series are dependent,the past observations may be used to predict future values. Ifthe prediction is exact, the series is said to be deterministic.We cannot predict a time series exactly in most practicalsituations. Such time series are called random or stochastic,and the degree of their predictability is determined by thedependence between consecutive observations. The ultimatecase of randomness occurs when every sample of a randomsignal is independent of all other samples. Such a signal,which is completely unpredictable, is known as White noiseand is used as a building block to simulate random signalswith different types of dependence. To properly model andpredict a time series, it becomes important to fundamentallyand thoroughly analyze the signal it self, and hence there is astrong need for signal analysis.
