__Time Series__

When data collected over a regular period of time (years, months, days, hours etc) such that it can be studied to derived hidden and meaningful results which can be further used to predict a future value. Example GDP, stock prices, monthly/quarterly sales etc.

Time series is finding its ways in various fields of business from predicting future stock price movement to calculating weather forecast. From forecasting sales of a product to studying the traffic on our website its found everywhere.

Time series can be used as a forecasting measure if the data collected is stationary.

For series to be stationary it needs to follow three basic criteria:

- Constant Mean: which means that at what point we study the series the mean should remain the same. Such a series will always return to its mean or would be mean reversing.

The first graph shows a mean reversing series. While the bottom graph shows a series which has an increasing mean as we move ahead with time. A series with time varying mean is said to be non-stationary

2. Constant Variance: which means fluctuations around the mean tend to be constant. A series where the variance is not constant is said to be non-stationary.

The first graph shows a stationary series with constant variance around the mean

3. Constant auto-covariance: which means that co-variance between time t and t+1 should be same as co-variance between time t+k and t+k+1, i.e. is should not increase or decrease with time rather should be same across the time period we are studying.

Here the first graph shows that the amplitude changes with time i.e. its time variant. However in the second graph we see its not time variant, rather the peak can be seen at regular intervals.

If a series follows above mentioned rules, its said to be stationary. Its important fora series to be stationary in order to build a time series model.

This article covers the basic assumptions for time series modelling. As we move forward with this series we will cover other important topic related of TS modelling like what is Random walk? How do we use dickey-fuller test? What is an ARIMA model?

Stay tuned for more articles on Time Series.

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