2.0 Forecasting Supply


2.1 Overview


In order to have more control over the security of supply, information is the key. The more information one has regarding supply and demand, the better one is able to plan one’s operations to avoid being unable to meet customer orders, or extra costs associated with excess inventory on hand. Three models were developed using Dynamic Regression:


        I.      A model to forecast daily supply for a forecasting horizon of up to about one week

     II.      A model to forecast daily supply for a forecasting horizon of up to one year

   III.      A model to forecast monthly supply for a forecasting horizon of up to 6 months


2.2 Model I and II  - Dynamic Regression


 A Dynamic Regression model states how an output variable is linearly related to current and past values of one or more input variables. It also takes into account the possible autocorrelation pattern of the disturbance series - Pankratz A. Forecasting with Dynamic Regression Models, John Wiley & Sons, Canada (1991)

In normal regression model where there is a dependant variable Y and a set of independent variables Xi. Dynamic Regression takes this one step further by modeling the errors of the model as an ARIMA model. The form of the model is:



μ is the constant, ωi are the coefficients for explanatory variables Xi,t-j,  θ and Ф are coefficients to model the error, at, where B is the backshift operator. The first part of the model is basically a simple linear regression model, and the second term is the ARIMA error term.

Through research, investigation and meetings with the clients, a pool of potential explanatory variables were established that may help in forecasting daily LPG supply from Maui. The approach taken with building the final Model I and II, was to put one variable at a time into a pool of variables available for selection into the model – similar to forward selection when building simple linear regression models. After an initial model is selected by Forecast Pro, the model is fine-tuned by adding in other significant variables, one at a time as suggested by Forecast Pro (these tend to be lags of the explanatory variables in the model so far, or perhaps a variable which is taken out, later to be put back in). Any non-significant variables identified after each insertion of a significant variable, is taken out one at a time (in order of most non-significance), and the model updated (the coefficients and significance statistics for each variable) after each time. This is because taking all the non-significant variables all together can produce a different model, from when one is taken out at a time.

In order for these models to be of use, the explanatory variables need to be forecasted for the period of interest. Some of the variable in Model I and II were deterministic and did not need to be forecasted. For short term forecasting of daily LPG supply, temperature data, one of the variables in Model I, may be obtained easily from external sources such as the New Zealand Meteorological Service. Model II also uses temperature data, and would need daily temperature forecasts for a longer period into the future. For this, we developed several temperature forecasting models using ARIMA modelling. While on a day to day basis, our models would give inaccurate forecasts, over a period of time, the models were able to capture the behaviour of temperature, with their regular seasonal cycles and variation from day to day. Using these forecasts in Model II would give an idea of the future outlook of daily LPG supply.

The reason that Model I is limited to only short term forecasting is due to the inability to develop a good forecasting model for one of the explanatory variables in the model – MAUIMA, which is the average of the last seven days daily supply of LPG from Maui. For short term forecasting, Model I is better than Model II, and that is primarily due to this variable. ARIMA modelling was tried to forecast this variable but good forecasts for long periods into the future could not be obtained.


2.3 Model III – Forecasting Monthly Supply of LPG


LPG is the by-product of the natural gas production. Model III aims to predict the future LPG supply from Maui based on its natural gas production. Figure 1 shows three phases in this model. Phase one uses Dynamic Regression to predict the total gross natural gas production in New Zealand. Phase Two calculates the future gross natural gas production from Maui based on the results from Phase One. Phase Three completes this methodology by calculating the future LPG supply from Maui based on its predicted natural gas production.


Figure 1 - Model III


2.4 Conclusions, Limitations and Recommendations


Model I is the better of Models I and II for forecasting daily supply, if the forecasting horizon is less than about one week. While this model is useful for short-term planning, if one wanted to forecast a long enough period into the future, then this model is unsuitable. This is because in order to use Dynamic Regression, one also needs the forecasted values of the explanatory variables that are in the model for the period that we want to forecast the dependant variable. Due to the inability at this stage to develop a good model to forecast one of the explanatory variables in this model, this model is best used for short-term forecasting.

Model II attempts to rectify the problem of Model I, and was developed for the purpose of forecasting a long period into the future. These daily forecasts would be useful if one wanted to carry out analysis for long-term planning purposes. Orbit Systems Ltd[1] has developed a Simulation Model for the purposes of evaluating such things as the effect on storage levels under different configurations of shipping rules and different demand situations. A required input is daily supply data of LPG. Model II was developed as a complement to this Simulation Model.

Model III, a monthly supply model, was developed as a complement to a monthly demand model for LPG that had previously been developed by another party hired by Liquigas Ltd. This would be useful for Liquigas Ltd to plan its medium-term operations such as when to import LPG from overseas. While monthly supply may be estimated by summing up the relevant daily forecasts from Model II, Model III incorporates information regarding natural gas production, and uses a different forecasting approach from Model II. It was hoped this approach would give more accurate monthly forecasts.  

Whist several attempts had been made to produce accurate and precise forecasting methods for forecasting supply of LPG, several limitations hindered our capability to achieve this.

Firstly, the conversion rate between natural gas and LPG is only a rough average, given by our clients. Since Model III depends heavily on this to produce accurate forecasts, our efforts can only go so far when this piece of information is not precise. Even if we could develop models that proved precise and accurate when compared to the actual figures available for 2006, ‘unpredictable’ events in the future would cause our models to become obsolete. Currently, it is clear that Maui is depleting, but there is a possibility of new wells being drilled in the future, as mentioned by our clients. This will likely cause a sudden increase in the supply of LPG from Maui but after that initial increase, supply would steadily drop off again. The exact effect of a new well on supply is unpredictable at this stage due to lack of information.

Finally, assuming that new wells will not be built, the depletion of Maui is still difficult to forecast. Commenting on the power blackouts of California in 2001, Colin Campbell, a retired petroleum geologist, said:


“Gas depletes differently from oil. … There were no market signals of the approach of the cliff at the end of the plateau. It accordingly came without warning, causing prices to surge through the roof, and bringing power blackouts to California.”
Colin Campbell, 2001.


Due to the nature of natural gas, production is normally capped at far below capacity, leaving an in-built and unseen ‘balloon’ or spare capacity. Not knowing how much is left in the wells makes it difficult to predict when it could suddenly run out.

With the depletion of Maui, there are several possible suppliers that Liquigas Ltd could consider for the future. LPG could be increasingly imported from Australia. The Pohokura Gas Field has recently started operating (September 2006) but at this stage, is not producing LPG. This may change in the future. The Kupe Gas Project was recently given the green light to proceed with construction (June 2006) and is expected to be on-line by mid-2009. Since these events are yet to occur, there is uncertainty involved and there is a lack of information, analysis of future LPG supply for Liquigas Ltd cannot be carried any further.


Main Page

1.0 Background

3.0 Forecasting Demand

4.0 Evaluating Storage Facilities




[1] A consulting company that was contracted by Liquigas Ltd to do some consulting work for them including building a simulation model to mimic the rules and operations of the business.