**Time Series Analysis**

A time series is defined as a sequence of observations taken at regular intervals over a period of time. For example, for a project organization such as Rolls-Royce, the monthly demand data for a particular type of aircraft engine over the past ten years would constitute a time series. The main theme underlying time series analysis is that past behavior of data can be used to predict its future behavior. However, in order to use time series analysis, we need to know about the three of the important components that can constitute the time series of a project environment. These are trend, cycle, and the random components.

**Trend ** is the long term movement of data over time. This definition implies that time is the independent variable and the data or set of observations we are interested in is the dependent variable. When we track data purely as function of time, there are several possible scenarios. First, data may exhibit **no trend ** as shown in the example below. In this case data remains constant and is unaffected by time.

Time Period |
1 |
2 |
3 |
4 |
5 |
---|---|---|---|---|---|

Data Value |
30 |
30 |
30 |
30 |
30 |

The second possible scenario is ** linear trend. **In this case, data as a function of time has a linear relationship as shown in the example below. The table above shows that rate of increase data between successive time periods is a constant two units. This series is called an **Arithmetic
Progression**. It should be noted that data can also exhibit negative linear trend with a rate of decrease between successive observations.

Time Period |
1 |
2 |
3 |
4 |
5 |
---|---|---|---|---|---|

Data Value |
30 |
32 |
34 |
36 |
38 |

The behavior of data over time may also exhibit a trend pattern that is **nonlinear ** such as **exponential growth or decay **.
An example of observations that have an exponential growth pattern is shown in the table below. In this case, each successive data
value is twice its previous value. In this example each pair of successive observations have a common ratio. Such a series is called
a **Geometric Progression**.

Time Period |
1 |
2 |
3 |
4 |
5 |
---|---|---|---|---|---|

Data Value |
30 |
60 |
120 |
240 |
480 |

In the case of exponential decay, each succeeding observation decreases by some constant factor. This is another form of the Geometric Progression and a sort of pattern that is observed with such phenomena as the decay in radiation levels from nuclear activity. The measure frequently used in exponential decay is the "half-life." It is the time it takes for the dependent variable to decay to half its original value. An example of exponential decay is presented in the table below. In this example of exponential decay, the half-life is one period.

Time Period |
1 |
2 |
3 |
4 |
5 |
---|---|---|---|---|---|

Data Value |
400 |
200 |
100 |
50 |
25 |

**Seasonal variations ** can be another component of a time series. These are periodic, short term, fairly regular fluctuations in data caused by man-made or weather factors. The increase in demand for candies during the Christmas season is an example of seasonal variations in data. **Cyclical variations ** in a time series are wave-like oscillations in data about the trend line and typically have more than one-year duration. These variations are often caused by economic or political factors. **Random variations ** are variations in data not accounted for by any of the previous components of the time series. These variations cannot be easily predicted and are only after the fact. In forecasting, these variations are accounted for as an error term. The decrease in demand for a company's product due to a plant shutdown caused by a labor strike is an example of a random variation in demand.

In addition to the qualitative and quantitative classification discussed above, forecasting methods can also be classified based on time frame. These are short term and intermediate term forecasting methods. Forecasting for the long term is typically done using by the qualitative methods discussed earlier in this lesson. We will now explore the various forecasting techniques that can be employed for the short and intermediate term forecasting.