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Stationary Series There are three basic criterion for a series to be classified as stationary series: The mean of the series should not be a function of time rather should be a constant.
The variance of the series should not a be a function of time. This property is known as homoscedasticity. Following graph depicts what is and what is not a stationary series. Notice the varying spread of distribution in the right hand graph 3.
In the following graph, you will notice the spread becomes closer as the time increases. The reason I took up this section first was that until unless your time series is stationary, you cannot build a time series model.
There are multiple ways of bringing this stationarity. Some of them are Detrending, Differencing etc.
You might know the concept well. But, I found many people in the industry who interprets random walk as a stationary process. In this section with the help of some mathematics, I will make this concept crystal clear for ever.
Imagine a girl moving randomly on a giant chess board. In this case, next position of the girl is only dependent on the last position. You want to predict the position of the girl with time. How accurate will you be? Of course you will become more and more inaccurate as the position of the girl changes.
This is the randomness the girl brings at every point in time. Now, if we recursively fit in all the Xs, we will finally end up to the following equation: Er t Now, lets try validating our assumptions of stationary series on this random walk formulation: Is the Mean constant?
E[Er t ] We know that Expectation of any Error will be zero as it is random. Is the Variance constant? Hence, we infer that the random walk is not a stationary process as it has a time variant variance. Also, if we check the covariance, we see that too is dependent on time.
Let us introduce a new coefficient in the equation to see if we can make the formulation stationary.
Here we will interpret the scatter visually and not do any test to check stationarity. Here is the plot for the time series: Increase the value of Rho to 0.An Introductory Study on Time Series Modeling and Forecasting Ratnadip Adhikari R. K. Agrawal - 3 - Time series modeling and forecasting has fundamental importance to various practical different time series models is supported by giving the experimental forecast results, performed.
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