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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.
Likewise, seasonal differencing is applied to a seasonal time-series to remove the seasonal component. From the perspective of signal processing, especially the Fourier spectral analysis theory, the trend is a low-frequency part in the spectrum of a series, while the season is a periodic-frequency part.
The original model uses an iterative three-stage modeling approach: Model identification and model selection: making sure that the variables are stationary, identifying seasonality in the dependent series (seasonally differencing it if necessary), and using plots of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the dependent time series to decide which (if any ...
X-12-ARIMA can be used together with many statistical packages, such as SAS in its econometric and time series (ETS) package, R in its (seasonal) package, [6] Gretl or EViews which provides a graphical user interface for X-12-ARIMA, and NumXL which avails X-12-ARIMA functionality in Microsoft Excel. [7] There is also a version for MATLAB. [8]
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.
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.
Time series forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modelled as a stochastic process .
Seasonal subseries plots enables the underlying seasonal pattern to be seen clearly, and also shows the changes in seasonality over time. [2] Especially, it allows to detect changes between different seasons, changes within a particular season over time. However, this plot is only useful if the period of the seasonality is already known. In ...