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Seasonal adjustment or deseasonalization is a statistical method for removing the seasonal component of a time series. It is usually done when wanting to analyse the trend, and cyclical deviations from trend, of a time series independently of the seasonal components.
, the seasonal component at time t, reflecting seasonality (seasonal variation). A seasonal pattern exists when a time series is influenced by seasonal factors. Seasonality occurs over a fixed and known period (e.g., the quarter of the year, the month, or day of the week). [1]
The seasonally adjusted annual rate (SAAR) is a rate that is adjusted to take into account typical seasonal fluctuations in data and is expressed as an annual total. SAARs are used for data affected by seasonality , when it could be misleading to directly compare different times of the year.
Calculate another estimate of the trend using a different set of weights (known as "Henderson weights"). Remove the trend again and calculate another estimate of the seasonal factor. Seasonally adjust the series again with the new seasonal factors. Calculate the final trend and irregular components from the seasonally adjusted series.
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function.Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.
In time series data, seasonality refers to the trends that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly. Seasonality may be caused by various factors, such as weather, vacation, and holidays [1] and consists of periodic, repetitive, and generally regular and predictable patterns in the levels [2] of a time series.
Also, where the variations are significantly larger than the resulting straight line trend, the choice of start and end points can significantly change the result. That is, the model is mathematically misspecified. Statistical inferences (tests for the presence of a trend, confidence intervals for the trend, etc.) are invalid unless departures ...
The order p and q can be determined using the sample autocorrelation function (ACF), partial autocorrelation function (PACF), and/or extended autocorrelation function (EACF) method. [10] Other alternative methods include AIC, BIC, etc. [10] To determine the order of a non-seasonal ARIMA model, a useful criterion is the Akaike information ...