Introduction to Time Series Analysis

Time series is a sequence of data points organized in time order. Forecast of data by analyzing time-based data is Time Series Analysis. It helps us examine past behaviors and patterns to identify understandings that enforce quick decision-making.

For example: Forecasting future temperatures based on past temperatures recorded in a timely manner.

Time series analysis and forecasting have many applications: analyzing the sales of your retail chains, finding anomalies in the traffic you're getting to your servers, and predicting stock markets, to name a few. Time series forecasting is barely a new question in data science and statistics. The term is self-descriptive and has been on business analysts’ plans for years now. The very first occurrences of time series analysis and forecasting trace back to the early 1920s.

The first actual application of autoregressive models to data can be brought back to the work of G. U Yule and J. Walker in the 1920s and 1930s. During this time the moving average was introduced to remove periodic fluctuations in the time series, for example, fluctuations due to seasonality.

Components of Time Series

we usually look at 3 main components: seasonality, trends, and residuals. Below is a decomposed time series comprising all the components. It is not necessary for every time series signal to comprise all these components, but at least one of them is required to explain the behavior.

Trend – The long-term gradual change in the series. This is the simplest trend pattern, as it demonstrates long-term growth or decline.

Seasonality – Predictable, short-term patterns that occur within a single unit of time and repeat indefinitely.

Noise (error) – Random variation due to uncontrolled circumstances.

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Time series forecasting methods

Forecasting can be done by various methods like a very basic method such as Na?ve forecasting in which the predicted value is simply the value of the most recent observation. Another method is the average method, in which all forecasts are equal to the mean of all the historical data. The most used or apt method for forecasting is the smoothing method. Time series smoothing methods are designed to adapt to changes in the data over time. Smoothing reduces noise by taking averages of observations over multiple periods. The two most common smoothing methods are moving average smoothing and exponential smoothing.

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Moving Average Smoothing: The moving average method of forecasting again works on the principle of averaging the values but instead of taking the average of entire values we will take the average of fixed periods. For example, if we compute 3-MA, so the period will be 3 and we will take the average of the first three values and so on.

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Exponential Smoothing: This principle also works on the method of averaging but with a slight difference that the most recent values will be given more weightage as compared to the old ones.

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