Basic Concepts of Time Series

A time series is a sequence of numerical data points in successive order.
Each data point in a time series is associated with a specific moment in time.

Components of a Time Series

Trend: The long term movement in a time series data set.
Seasonality: Systematic, calendar related movements, usually seen as periodic and predictable fluctuations.
Cyclicality: Patterns that reoccur periodically but do not have a fixed period.
Random or Irregular movement: Unpredictable fluctuations that cannot be defined by systematic or calendar related elements.

Time Series Analysis

Time series analysis is the process of using statistical techniques to model and explain a time-dependent series of data points.
Its key purpose is to extract significant statistics and other characteristics of the data to predict future values.

Methods for Analyzing Time Series

Moving Averages: This technique involves taking the arithmetic mean of a set number of time periods, which then “moves” forward in time.
Exponential Smoothing: This method assigns exponentially decreasing weights over time. It’s often more responsive than moving averages as it gives greater weight to more recent observations.
Decomposition Methods: These methods aim to deconstruct a time series into trend, seasonal and random components.

Forecasting from a Time Series

Forecasting involves predicting the future values of a time series. It is key for many areas of business and strategic planning.
Accuracy of forecasts can be determined using measures like Mean Absolute Deviation (MAD), Mean Squared Error (MSE) or Mean Absolute Percentage Error (MAPE).

To excel in time series analysis, remember to not only focus on the formulas, but to also understand fundamentally what a time series is and how different components interact to create the overall behaviour of the series. It’s a deep topic with ties to many real-world applications, so practise solving problems from past papers and make sure you understand the concepts fully!