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Chapter 8

Introduction to Time Series Analysis: Hidden Patterns in Time

#Time Series#Stationarity#Autocorrelation#ARIMA

Time Series Analysis: Speaking of Tomorrow with Yesterday’s Data

Data observed over the ‘course of time’—such as stock prices, exchange rates, or monthly sales—is called time series data. Unlike typical independent observations, time series data possesses ‘autocorrelation,’ where past values influence future ones.

1. The Four Components of Time Series Data

The complex graphs we see are actually a combination of four distinct rhythms.

Components of Time Series Analysis

ComponentMeaningExample
TrendLong-term upward or downward movementPopulation growth, technological advancement
SeasonalityPatterns that repeat at fixed intervals (yearly, weekly, etc.)Air conditioner sales in summer, weekend restaurant activity
CycleUp and down movements without a fixed periodEconomic cycles, real estate market
IrregularFluctuations caused by unpredictable eventsPandemics, sudden wars

2. Prerequisite for Time Series Analysis: Stationarity

For a model to forecast the future accurately, the statistical properties of the data (mean, variance) must remain constant over time. This is called Stationarity. If a trend exists, we start the analysis by making the data ‘stationary’ through ‘differencing.‘

3. Three Stages of ARIMA Modeling (Box-Jenkins Method)

The most representative time series model, ARIMA (Autoregressive Integrated Moving Average), is finalized through the following process:

1
Identification

Look at ACF and PACF plots to determine the orders of AR and MA components.

2
Estimation

Estimate the model's parameters using methods like Least Squares.

3
Diagnosis

Ensure the residuals (errors) show no patterns and are 'White Noise'.

4. Visualizing Seasonal Patterns

Below shows a typical seasonal pattern found in monthly sales data for a specific product.

Monthly Ice Cream Sales Trend (Seasonality Example)

It shows a clear rhythm peaking during summer months (July-August) and dropping in winter.


💡 Professor’s Tip

The first rule of time series analysis is to “plot the graph.” Visually identifying trends or seasonality before performing statistical tests accounts for more than half of the analysis. A time series analyst is like a conductor reading the rhythm of data.

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