Time series analysis is that type of analysis that deals with time series data. The time series data in time series analysis usually involves price data of certain commodities, or stock exchanges, like the Bombay Stock Exchange (BSE) and the New York Stock Exchange (NYSE).
There are many concepts used in time series analysis. One such process is a random process or a stochastic process in time series analysis. This is a collection of random variables that are ordered with respect to the time. For example, if Y is a random variable, in the case of continuous nature, it will be denoted as Y(t), and in the case of its discreet nature, it will be denoted as Yt in time series analysis.
In time series analysis, it is very important for the analyst to know that before conducting time series analysis, the stochastic process should be made stationary. A stationary process in time series analysis is said to be stationary only if the mean and variance is constant over the time, and if the value of the covariance between the two time periods mainly depends upon the distance between the two time periods. It is important for the analyst to know the reason behind stationary stochastic process in time series analysis. The reason is that it is not practically possible to compute mean and variance for every time period in time series analysis. If the time series is not stationary, then it will give the value of mean and variance for that particular time series.
A stochastic process in time series analysis is said to be purely random only if it has the mean as zero and the variance as constant. Additionally, it must be serially uncorrelated.
Differencing is one of the methods in time series analysis that helps in making the volatile time series into a stationary one. There are different orders of differencing in time series analysis. Suppose, for example, that the volatility is not reduced from the data after first order differencing. In this case, the analyst can make a second order differencing, in order to achieve stationarity in data in time series analysis.
In time series analysis, the exponential smoothing method predicts the next period value on the basis of the past value and the current value. In time series analysis, this method is used to make short term predictions about the commodities or the stock exchanges. Alpha, Gamma, Phi, and Delta are the parameters that are used to estimate the effect of the time series data in time series analysis. In time series analysis, alpha is used when seasonality is not present in the data. In time series analysis, Gamma is used when the series exhibits certain trends in the data. Delta is used in time series analysis when seasonality cycles are present in data. In time series analysis, the various models are applied according to the exhibition of the pattern in the data.
The major goal of time series analysis is to fit the data to the appropriate model under consideration.
There are certain assumptions made in time series analysis. These assumptions are as follows:
In time series analysis, the first assumption is that the series should be stationary. In other words, it means that in time series analysis, the series are normally distributed and the mean and variance is constant over that period of time.
In time series analysis, it is assumed that the error term is randomly distributed and the mean and the variance are constant over a time period. The errors in time series analysis are assumed to be uncorrelated to each other.
In time series analysis, it is assumed that no outlier is present in the series. The presence of outliers affects the inference of the data in time series analysis and thus leads to inaccurate results. If shocks are present in the time series analysis, they are assumed to be randomly distributed with a mean zero and a constant variance.
