Time Series Analysis
What is Time Series Analysis?
A sequence of data points measured at successive points in time, typically at uniform time intervals.
Key formula / rule: Simple Moving Average (SMA)
Key points
- Define what a time series is and its purpose.
- Identify and differentiate between the four main components of a time series.
- Understand the additive and multiplicative models for time series decomposition.
- Explain the basic application of moving averages in time series smoothing.
Common exam trap
Confusing seasonal and cyclical components (seasonal is fixed period, cyclical is not).
Definitions
- Term
Time Series
- Meaning
A sequence of data points measured at successive points in time, typically at uniform time intervals.
- Term
Trend
- Meaning
The long-term general direction or movement of a time series, indicating growth, decline, or stability.
- Term
Seasonal Component
- Meaning
A pattern in a time series that repeats over a fixed and known period, usually within a year (e.g., monthly, quarterly).
- Term
Cyclical Component
- Meaning
Fluctuations in a time series that are longer than a year and are not of a fixed period, often associated with economic cycles.
- Term
Irregular Component
- Meaning
The unpredictable, short-term fluctuations in a time series caused by random or unforeseen events, also known as random variation or noise.
- Term
Moving Average
- Meaning
A statistical technique used to smooth out short-term fluctuations in time series data and highlight longer-term trends or cycles by averaging data points over a specified period.
Learning objectives
Define what a time series is and its purpose.
Identify and differentiate between the four main components of a time series.
Understand the additive and multiplicative models for time series decomposition.
Explain the basic application of moving averages in time series smoothing.
Interpret simple time series graphs to identify trends and seasonal patterns.
Formulae
- Name
Simple Moving Average (SMA)
- Note
Where Xt is the data point at time t, and n is the number of periods over which the average is calculated. Used for smoothing time series data.
- Expression
SMAt = (Xt-n+1 + Xt-n+2 + ... + Xt) / n
- Name
Additive Time Series Model
- Note
Used when the magnitude of seasonal and cyclical fluctuations does not depend on the level of the time series.
- Expression
Yt = Tt + St + Ct + It
- Name
Multiplicative Time Series Model
- Note
Used when the magnitude of seasonal and cyclical fluctuations depends on the level of the time series.
- Expression
Yt = Tt × St × Ct × It
Prerequisites
Basic understanding of statistical averages (mean, median).
Familiarity with graphical representation of data.
Conceptual knowledge of data patterns and variations.
Common mistakes
Confusing seasonal and cyclical components (seasonal is fixed period, cyclical is not).
Applying an additive model when a multiplicative one is more appropriate, or vice-versa.
Ignoring the irregular component, which accounts for unexplained variation.
Using an inappropriate smoothing window for moving averages, leading to over-smoothing or under-smoothing.
Keywords
Time Series
Trend
Seasonality
Cyclical
Irregular
Forecasting
Moving Average
Additive Model
Multiplicative Model
Decomposition
Practice preview
If a time series shows a consistent upward movement over several years, what component is primarily being observed?…
medium
Seasonal variations in a time series are typically caused by:…
easy
Which of the following statements about time series decomposition is INCORRECT?…
medium