QUESTION:

We often have the problem to model or analyze data that is collected at unequally spaced times. For example, the demand pattern might be such that a RANDOM INTERVAL occurs before a DEMAND is measured or arises. Consider the time series of GAS USEAGE where a number of days exist between trips to the gas station. Upon arrival at the gas station the customer purchases an amount of gas. This example of UNEVEN or UNEQUAL time intervals is quite common. What to do? How to analyze?

ANSWER:

This example focuses on how an approach to modeling a time series that is riddled with omitted or non-events. The literature of how to analyze time series when you have omitted data is sparse and complex. One straight forward approach is to follow the outline in this example. Consider the demand for a product in which the time between orders is a random variable and the number of orders received is also a random variable. This could also be the occurrence of deaths of a rare disease or the modeling of failure data. The literature refers to these cases as D.A.R.I.M.A. For discrete autoregressive integrated moving averages. The following is the recent sales of a product to a customer who periodically, i.e. a random time interval, has ordered a product. This happens to be oil delivery to a specific customer.

0 0 0 1 0 0 2 3 0 0 0 0 0 0 0 0 1 4 0 0 2 0 6 0 0 2 12 0 0 0 0 0 0 1 0 0 2 3 0 0 0 0 0 0 0 0 1 0 0 0 0 0 3 0 0 0 0 5 0 0 1 0 0 0 0 0 3 5 0 0 0 0 0 0 1 0 3 0 0 0 7 0 0 0 3 0 0 0 1 0 3 0 1 0 4 0 0 0 2 0 0 0 0 3 0 1 0 0 2 3 0 0 0 0 0 0 0 0

For example, three days went by before the first order. The customer ordered 1 unit and then two days elapsed. On the next day, he ordered 2 units and on the very next day order three units, etc. We have 118 days of order information. Note:the actual order days were:
1,2,3,1,4,2,6,2,12,1,2,3,1,3,5,1,3,5,1,3,7,3,1,3,1,4,2,3,1,2,3
This sequence can't be treated as an ordinary uninterrupted time series because of the non-constant time differential. Additionally the treatment of small integers as if they were continuous, stretches one of the assumptions underlying continuous distribution modeling. Consider creatin a series which is the time between orders and relate that series to the rate (y) where rate is based upon the number of units ordered and the number of days since the last order. The x variable is the number of periods(days) since the last order.

For more details on the analysis of this data , please download ....... SPARSE.ZIP