Time series analysis comprises of methods for analyzing time series data to extract meaningful statistics and other characteristics of the data.Sobu and Wu (2012), Kang et al. (2011), Mori and Takahashi (2012). The main types of time series models include—parametric and nonparametric time series models. The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters Huang and Lu (2010). All the time series models used in this paper are parametric models, described as below Douglas and Kulahci (2008).
Single, double, centered and weighted moving average models were tested for the available data with different orders and intervals. It was observed from the analysis that the value of interval, when chosen to be small (that is, less than 11), the predicted values and the actual values in the test data were closely similar. Though the predicted values are good for higher values of wind speed, when predicting lower values, the moving average model of very small interval tends to saturate towards a constant value. Hence, exponential smoothing methods were developed. The models are developed using Rsoftware and Microsoft Excel Zhao (2012).
Single exponential smoothing (SES)
Exponential Smoothing is a class of methods that imply exponentially decreasing weights as the observations get older. They have a common property that recent values are given relatively more weight in forecasting than the older observations. The model assumes that the data fluctuate Lim (2011) around a reasonably smean (no trend or consistent pattern of growth).
SES model is formulated as indicated in Eq. 1
$$\begin{aligned} S_{t+1}{ \,= \,}\alpha \times x_{t}+(1\alpha )\times S_{t} \end{aligned}$$
(1)
where \(S_{t+1}\) = next forecast value of the variable, \(S_t\) is the present forecast value of the variable, \(X_t\) is the present actual value of the variable, \(\alpha\) is a constant between 0 and 1.
Double exponential smoothening (DES)
This method is used when the data show a trend. Exponential smoothing with a trend works much like simple smoothing except that two components must be updated each period—level and trend. The level is a smoothed estimate of the value of the data at the end of each period. The trend is a smoothed estimate of average growth at the end of each period. DES can be modeled as given in Eqs. 2 and 3
$$\begin{aligned} {\mathrm{Level}}{:} \,S_{t+1}{\, = \,} \alpha X_{t}+(1 \alpha )(S_{t1}+ b_{t1}) \end{aligned}$$
(2)
$$\begin{aligned} {\mathrm{Trend}}{:}\, b_{t}{ \,= \,} \beta (S_{t}S_{t1})+(1\beta ) b_{t1} \end{aligned}$$
(3)
Triple exponential smoothening (TES)
This method is used when the data show trend and seasonality. To handle seasonality, a third parameter is added. Now, a third equation is introduced to take care of seasonality. The resulting set of equations is called the “HoltWinters” (HW) method after the names of the inventors. The model is given by Eqs. 4, 5 and 6
$$\begin{aligned} {\mathrm{Level}}{:}\, L_{t}{\, = \, } \alpha (Y_{t}S_{ts})+(1\alpha )(L_{t1}+b_{t1}) \end{aligned}$$
(4)
$$\begin{aligned} {\mathrm{Trend}}{:}\, b_{t}{\, =\, } \beta (L_{t}L_{t1})+(1\beta )(b_{t1}) \end{aligned}$$
(5)
$$\begin{aligned} {\mathrm{Seasonal}}{:} \,S_{t}{ \,= \,} \gamma (Y_{t}L_{t})+(1\gamma )S_{ts} \end{aligned}$$
(6)

\(\alpha\) is the level smoothing constant (lies between 0 and 1).

\(\beta\) is the trend smoothing constant (lies between 0 and 1).

\(\gamma\) is the seasonal smoothing constant (lies between 0 and 1).

\(L_{t}\) is the estimate of the level of the series at time t.

\(Y_{t}\) is the actual value of the series at time t.

\(b_{t}\) is the estimate of the slope of the series at time t.

\(S_{t}\) is the seasonal component.

s is the length of seasonality.

m is the number of periods ahead to be forecast.

\(F_{t+m}\) is the forecast for m periods ahead.
The forecast is obtained from the level, trend and seasonal components as in Eq. 7
$$\begin{aligned} {\mathrm{Forecast}}{:} \,F_{t+m}{ \,= \,} L_{t}+b_{tm}+S_{ts}+m \end{aligned}$$
(7)
Decomposition model
It is possible to decompose time series data into various subcomponents to see how these components affect the data in the series. Time series data are mainly composed of seasonal pattern and trend pattern. There are two different decomposition models possible.

1.
Additive Decomposition: Here, the total data are taken as the sum of the decomposed patterns
Xt = seasonal (St) + trend (Tt) + random.

2.
Multiplicative Decomposition: Here, the given time series data are treated as the product of the decomposed patterns
Xt = seasonal (St) \(\times\) trend (Tt) \(\times\) random.
Additive decomposition is effective when the peak values of the seasonal data do not vary much. Multiplicative models are effective when the seasonal value changes over time. Both additive and multiplicative models were tested for the available data. It was found that the multiplicative model works well. The reason could be that the wind speed changes with the change in weather. Fig. 1 shows the decomposition of wind speed for the month of May 2013 using R.
Forecasting the decomposed seasonal and trend patterns separately to predict the wind speed worked very well. This analysis was done in Microsoft Excel. The following procedure was used for the forecast. The data were smoothened by taking the centered moving average. The interval for centered moving average was taken as 144 samples which correspond to samples at every 10 min for each day. The detrended series is calculated by dividing the smoothened series from the actual data. The seasonal component for each 10min sample is estimated by averaging the detrended values for that particular time of each day. The total seasonal pattern is obtained by stringing together all the seasonal indices for each day of the data. The forecast for the seasonal component can easily be estimated by extending the seasonal pattern to the next day. The forecast for the deseasonalised data is obtained by developing exponential smoothing model for the deseasonalised data. This hybrid model was tested for various data sample durations, like 1 month, 2 months and 4 months. The steps involved in developing the multiplicative decomposition model are listed below.

1.
Obtain the trend pattern by calculating the centered moving average for the entire data.

2.
Find out the detrended pattern by dividing the total data by the trend series.

3.
Seasonal component is calculated by averaging the detrended values for that particular time of all the days.

4.
Calculate the deseasonalised data by dividing the seasonal data from the actual data.

5.
Bring out a single exponential model for the deseasonalised data.

6.
Forecast seasonal data by extending the data for the next day.

7.
Forecast deseasonalised data by forecasting the exponential smoothing model.

8.
Multiply both the forecasted data to get the forecast for the actual data.