Time Series Analysis Introduction Essay Example

St* Ct *It or Yt = Tt +St +Ct +It

Where Yt = Actual value of the data in the time series at time t Tt = Trend value at time t St = Seasonal variation at time t Ct = Cyclical variation at time t Rt = Random variation at time t Depending on the kind of time series being calculated, the formula might be additive or multiplicative. Trend A trend is a relatively smooth long-term movement of a time series. It is the first basic element that affects data collection in time series analysis.

It can be described as the growth or decay tendencies for data to increase or decrease fairly steadily over a period of time. Long-term trend is typically modeled as a linear, quadratic and exponential function.

When a repetitive pattern is observed over some time horizon, the series is said to have seasonal behavior. It is usually associated with calendar or climatic changes and is frequently tied to a yearly cycle, which regularly fluctuates and repeats yearly about the same time and level of intensity.

Cyclical variation is an upturn or downturn not tied to seasonal variation but usually results from changes in the overall economic conditions such as recession and expansion.The first three components are deterministic which are called “Signals”, while the irregular component is a random variable, which can be described as any fluctuation not classified as one of the previous elements. It is unexplainable therefore it is unpredictable. Decomposition Procedure To be able to make a proper forecast, we must know to what extent each of the above components is present in the data.

Hence, to understand and measure these components,

the forecast procedure involves initially removing the component effects from the data (decomposition). After the effects are measured, making a forecast involves putting back the components on forecast estimates (recomposition). The time series decomposition process is depicted by the following flowchart: The first step of a time series decomposition is to identify and remove seasonal effects in the data in order to calculate the trend. It is also called smoothing process. The general idea is to present the data as it would have appeared without the tainting effects.

We also can use simple moving average or exponential smoothing to make forecasts for the next few periods. The procedure is just like we did in decomposition. Moving Averages: Moving Averages (MA) is an effective and efficient method provided the time series is stationary in both mean and variance.

Et+1= (Xt + Xt-1 + ••• +Xt-N+1)/N

Where Et+1 = Forecast for the next period (t+1) Xt, Xt-1 = Actual values at their respective times N = Number of observations included in the average When we use moving average to forecast, we must first decide how many observations to use in the moving average. The larger the number of observations in the average, the greater the smoothing effect.