Seasonal Adjustment

Seasonal adjustment is a statistical technique used to remove the effects of regular, repeating patterns (seasonal variations) from a time series dataset. Seasonal variations refer to the predictable fluctuations or patterns that occur at specific intervals, often corresponding to certain times of the year, months, weeks, or days. These patterns can obscure the underlying trends and make it challenging to analyze the true behavior of the data.

The primary goal of seasonal adjustment is to isolate and understand the non-seasonal components of a time series, such as trends and irregular fluctuations. This process allows for a clearer analysis of the underlying patterns, making it easier to identify long-term trends, make accurate forecasts, and detect unusual events.

Key steps in seasonal adjustment include:

1. Identifying Seasonal Patterns:
   • Analyze the time series to identify repeating patterns that occur at regular intervals. These patterns may be related to seasons, holidays, or other periodic events.
2. Decomposition:
   • Decompose the time series into its different components, typically separating it into trend, seasonal, and residual (error) components. The trend represents the long-term movement, the seasonal component captures the repeating patterns, and the residual component includes the irregular fluctuations.
3. Adjustment:
   • Adjust the time series by removing or smoothing out the seasonal component.

Decomposing Time Series

Seasonality in time series can be represented by breaking it down into a trend component, a seasonal component, and an irregular component. There are several methods to decompose a time series into its trend, seasonal, and residual components. The most common approach is Additive Decomposition.

Additive Decomposition

where,

• is the actual value of the time series at time t.
• is the trend component at time t.
• is the seasonal component at time t.
• is the irregular(error) component at time t.

The additive decomposition assumes that the effects of trend, seasonality, and residuals are separate and non-interacting. The observed value at any given time is the sum of these three components. This model is appropriate when the impact of each component on the total value is considered to be independent and straightforwardly additive.

Trend Estimation

Compute the moving average to capture the trend. We can use a simple moving average or other techniques like exponential smoothing. Here, we’re using moving average.

The trend component represents the long-term movement or underlying growth/decay pattern in the time series. It reflects the overall direction in which the time series is heading, abstracting from short-term fluctuations.

In an additive decomposition, the trend component contributes to the total value independently of the other components. The moving average is a common technique used for trend estimation in time series analysis.

The moving average is computed by taking the average of the values over a specified number of periods, which is m in this case.

Where,

•  the value at time t.
• k is the number of periods in the moving average.

It is particularly useful for removing short-term fluctuations and highlighting the overall direction of the data.

Compute Detrended Series

Subtract the moving average from the original time series to obtain a detrended series.

Calculate the Seasonal Component

The seasonal component represents the average pattern or deviation from the overall trend that occurs in each season across multiple years. It helps identify recurring patterns or cycles that are not part of the long-term trend.

Where, n be the number of seasons.

The choice of n depends on the periodicity of the seasonality in the data. For example, if you observe a yearly seasonality, n would be set to 12 for monthly data.

Calculate Residuals

Residuals represent the remaining variation in the time series after accounting for both the trend and the seasonal component.

It helps defining the unexplained variation or noise in the time series data Residuals are important for model diagnostics and validation. A good forecasting model should have residuals that are random and show no discernible pattern. If patterns are present in the residuals, it suggests that the model may need further refinement.

This is most suitable when the seasonal fluctuations remain constant in size regardless of the overall level of the series. Alternatively, there is a multiplicative form of this decomposition that may be more appropriate depending on the characteristics of the data and the relationship between the components.

Why it is important to adjust seasonal variation?

Seasonal changes are important for a number of reasons:

1. Finding Trends and Cycles: Seasonal adjustments make it easier to see underlying trends and cyclical swings in the data by eliminating seasonal patterns. This is especially crucial for economic data as seasonal variations may obscure significant trends in employment, sales, and other economic metrics.
2. Comparing Data Points: Seasonal adjustments allow for meaningful comparisons between data points from various time periods or seasons. Due to the impact of seasonal changes, comparisons may be deceptive in the absence of seasonal adjustments.
3. Forecasting and Analysis: Seasonal adjustments enhance the precision of statistical studies and forecasting models. These models are more effective at identifying underlying patterns and correlations in the data by eliminating seasonal noise.

Advantages of Seasonal Adjustment

• Better Forecasting: By exposing underlying patterns and trends that are independent of seasonal variations, seasonal adjustment enables more accurate forecasting.
• Improved Trend Analysis: By separating the impacts of seasonality, it makes it easier to comprehend and analyze long-term patterns in the data.
• Comparability: Since seasonal influences are eliminated, seasonally adjusted data facilitates the comparison and analysis of various time periods.

Disadvantages of Seasonal Adjustment

• Assumption of Consistency: Seasonal adjustment is predicated on the idea that seasonal patterns would stay mostly unchanged over time. This assumption may not hold true if there are substantial changes in the underlying environmental or economic circumstances.
• Data Smoothing: The data is smoothed throughout the seasonal adjustment process, which may cause certain short-term swings to be lost and make it more difficult to spot abrupt shifts or abnormalities.
• Complexity: The implementation of some sophisticated seasonal adjustment methods might be challenging and call for a solid grasp of statistical methodology.

Time series data can be difficult to evaluate successfully because of the patterns and trends it frequently displays. To address these tendencies and improve the data’s suitability for modeling and analysis, two strategies are employed: seasonal adjustment and differencing.