Time Series Forecasting - Final Paper
BUS/461 - Applied Management Science
Introduction
When we observe events on a timely manner, this is called time series prediction
also known as a part of forecasting, or predicting an outcome in the future based on the
information from the past (Lawrence & Pasternack, 2002, p. 387). Time series then
involves basic information and data from the collective past and these are used, analyzed
and reviewed to predict the future of a specific product or say service. Time series
forecasting is important in making business decisions hence it is important that the
forecasting must be made precisely and correctly. Among the things we are hearing being
forecasted are the weather, future sale of a particular product or the coming temperature.
There are different time series forecasting modelling and in this paper, we will discuss the
importance of such information and how it is being used. In the end, we will be providing a
recommendation based on the conclusion that we will have on this paper.
The Importance of Time Series Data
The most important use of time series forecasting is to be able to predict a certain
future involving the product or service that the company is providing, in case a prediction
is inline, then it means that the company can now see possible problem or issues in the
future that they can address in advance. Besides, if they can address issues in advance, the
company can avoid losing more because they can have a backup plan all the time. One
company that uses forecasting all the time are BPO or call centers where in the volume of
calls that the company might need to answer over a period of time is being forecasted in
advance so the company can provide enough number of people to answer it. This means
effectively utilizing the resources and manpower that the company has while at the same
time being able to identify if each employee got all the tools they need in order to do their
work. Tools like computers, chairs and tables are all necessary in order to make each
individual employee function properly.
Aside from industry needs and corporate needs, there are other sector of the
community that uses forecasting and time series to be a useful part of humanity. Take for
example the scientific discoveries that we have in the past, the different diseases and
medical conditions that we have recorded and the different medications and researches
done to cure such medical condition. All of these are being reviewed and analyzed to get
better information about different current medical conditions that we have at the moment.
In cases where in gaps are visible, there is a big chance that filling such gap can actually
resolve the problem or the current condition that the doctors are trying to identify.
If there are statistics and data that need to be reviewed, time series can be used to
make sure that these data do correlate with each other in any way (Brillinger, 2000).
Besides, time series data is not an ordinary set of number but is in fact a data that means to
communicate and provide information.
Components of Time Series Data
Time series can be computed in different ways using different values that are
present for the study. Among the things that can be looked at are long term trends of a
particular product like sale in ten years, seasonal variations, random effects and cyclical
variation (Lawrence & Pasternack, 2002, p. 387). (Lawrence & Pasternack, 2002).
Long Term trend
When there is a slow evolving process in a certain period of time, long term trend
analysis can be used. The result on this analysis can be a good one or a bad one (upward or
downward trend) or sometimes it can be no change at all. When a trend is not showing any
changes, it is called stationary trend but when there are a lot of change, it is called nonstationary. For non-stationary data, it means that there are variables that changes from
time to time and that the variance varies as well. To check the validity of the variables,
correlation is being used. On the other hand, for non-stationary long trend time series, it
can be that the variables are not moving or it goes down to 0 (Pankratz, 1983). If the data
result in a time series forecasting is stationary, the autocorrelation must be estimated to
test the result's reliability. Using the Dickey-Fuller regression test is also possible where in
the model as follow can be used (Dickey & Fuller, 1979):
t = 1, 2, n. (1)
In this equation, the variable of interest will be Yt and the real number is
represented by Y0 = 0 with an error of 0 and at least 2 points variance. This equation can
be rewritten as (2).
H0: = 0 = null hypothesis
Seasonal Variation
When a change occurs on any of the variables that we have on the time series, this is
called a seasonal variation. The changes occurred must be on different seasons and time
series to call it seasonal variation. Seasonal variation can happen regardless of how long
the time frame is between the changes and when it occurred so it can be between a few
days or weeks or even longer. Longer variations are like demands for turkey which is very
high during thanksgiving where in almost every American family celebrates it with a turkey
hence a lot of order for a turkey meat needs to be met. Some of the seasonal variations that
we are experiencing are also for demands in cars which according to the data of GM
happens to be high for some time of the year. A graph is normally used to show all data.
From the graph, the entire data can be seen hence a particular movement at a specific date
of the year or month can be seen leading to the conclusion of the time when a particular
product sale would go high or low.
Cyclical Variation
In this variation, it means there are no patterns as to when change will happen.
Random Effects
When time series variables changes without any specific pattern, we call random
change. During a random change pattern, there are variables that need to be constant and
independent while one specific variable changes all the time. The use of small-shuffle
surrogate (SSS) is used to test for any random effects in time series data (Nakamura &
Small, 2007). Using the SSS though is not dependent on the way the information is being
distributed (Nakamura & Small, 2007).
Forecasting Using Time Series Data
Forecasting is a two-step method where in the first step to work on the data is
needed for the time series. Prior to collecting the data, the time or the length of time for the
data collection must be set first whether it will be a weekly or a monthly data collection.
With the data at hand, you can now determine the type of time series method to use. With
the present data, certain hypothesis must be given as well. Once data is gathered, the next
important step to take is to select the best model of time series to use for forecasting
purposes. There are variables that you need to consider prior to selecting the time series
method that you will use and there are models that varies because of certain factors. If you
have stationary time series, then you will require a mathematical model to make it work
while seasonal time series requires a different model. Lastly, once you have the model and
the data at hand, you can now begin with your forecasting work.
Forecasting Methods
There are different forecasting methods that we have and each method varies from
one another and can be used depending on some variables that we currently have. Let us
take a look at the most common forecasting methods we have.
Chatfield (2001) identified three forecasting methods that are commonly used =.
They are judgmental forecasts, univariate forecasts and multivariate forecasts.
When we say judgmental forecasts, the forecasts will be based on the intuition or
tacit knowledge of the person or the subjective input of the person. Relevant information is
used as well.
Time series is also called as univariate method of forecasting where in the data from
the past is being used believing that there are similarities from the past to the current
trends in the market.
If there are more values or factors being considered in the time series predictions,
then multivariate methods are being used. In this model, there are different models being
used and different equations yet the variables used are dependent on each other (Chatfield,
2001, p.12). (Chatfield, 2001).
In this paper, we will focus on the methods of univariate time series.
One sample is the long term trend within a stationary time series where in there is
just three or less equations used (Lawrence & Pasternack, 2002, p. 390).
(3)According to Lawrence & Pasternack (2002, p. 390), t can represent the value of
time series with a random error if the mean is stationary. Random error here are 0 and are
independent. If you will be doing a long term analysis here, the trend doesn't change and is
constant.
(4) In equation 4, there is a linear equation because of the coefficient used, because
there are different values used aside from 0, the time series is no longer stationary. When
there are errors randomly distributed, the trends on the time series can be checked using a
linear regression.
For seasonal time series forecast, it should be first identified whether it is an
additive or a multiplicative meaning additive seasonality is when the mean doesn’t affect
the variation while multiplicative variation is when the mean is proportion or doesn't
change (Chatfield, 2001, p. 30). According to (Chatfield, 2001, p. 30). Equation 7 can be
used to forecast additive seasonality.
(5) There represents the value of the time series while seasonal index is the mean of
the series. There is a random error as well. Using equation five, additive series can be
forecasted too if some values gets modified through logarithmic transformation.
(6) If you are doing a time series forecast with something of a random effects then
you will use a random walk model given with the following formula x(t+1) = x(t) + (t) (7)
(Chatfield, 2001; Spitzer, 2001).
There will be the value of t as the independent variable and the IID or the identically
distributed noise. When the value of t is represented by zero, then the drift is considered to
be random. Model 7 is not stationary but it can be transformed into a non-stationary by
putting in different values (Chatfield, 2001, p. 38). Differencing is a method of making
stationary series a non-stationary and a second differencing is normally encouraged to
attain such effect. The Box-Jenkins methodology which uses Autoregressive Moving
Average (ARMA) or Autoregressive Integrated Moving Average (ARIMA) is one of the most
common forecasting methods being used today. With the use of ARIMA, there are things
that can be performed like estimating model parameters and doing residual analysis using
the two terms of ARIMA methods (Hyndman, 2001). The two terms of ARIMA are the
autoregressive term and the moving average term. The first term means that the data used
for predictions are based from the past while the second term uses errors from random
data (Hyndman, 2001). There are 4 steps involved in the Box-Jenkins model. The first step
is identification where in relationship of data and the statistics they represent are being
checked. From there, data that will fit the model will be looked at and choose from. The
second step is estimation where in the models is being identified and estimated here. The
third step is diagnostic check to figure the adequacy of the statistical analysis done to the
values and the last one is forecasting or giving predictions based on the adequate analysis
made from step 3.
Forecasting method using the Box-Jenkins method is too popular among business
and healthcare providers and companies. There are programs and software applications
that use such and there are so many references that you can to review more information
about Box-Jenkins method (Pankratz, 1983).
Issues
Time series forecasting is not a 100% accurate that is why it is called forecasting
because there can be differences with the values being used like the time plotted and the
season used. There is also a problem if there are missing links or data necessary to make
the forecast. Accuracy can be sacrificed if there are missing data from the values being
used.
Forecasting is not just a prediction but it also lies on assumptions based on data
from the past and from estimations of the future. It means that using different methods for
estimation can mean different results and predictions. If there are new information coming
out, then it means that the forecast needs to be changed or modified as well (Chatfield,
2001, p. 16).
The data being used itself can be a problem as well when making forecasts. There
should be a random yet standardized collection of data during the data collection period.
Daily data for example should be collected at the same time of the day but sometimes when
people knew they are being observed and data are collected, they might tend to change
their behavior causing the data collection to change results.
Future Enhancements
The use of Box-Jenkins methodology can be a good enhancement for me since
almost every companies and corporation out there rely on it today when it comes to
forecasting. Also, there are a lot of new programs that can be used to make the Box-Jenkins
methodology more effective depending on the need of the company. Most programs today
just uses a software that can do the analysis and suggestion of model for the time series
then the forecast will be provided automatically. All you have to do with Box-Jenkins
method is to upload the data as needed.
Conclusion
Forecasting using the time series method is essential to almost all businesses out
there that I know. Forecasting and time series depends on different data gathered and used
and through time series, it is expected that companies can make good decisions that will
benefit the company. With different methods to use for time series, it is important to be
aware of the advantages and disadvantages of it before using any.
References
Brillinger, D. (2000). Time Series: General. 1-22. Retrieved from
http://www.stat.berkeley.edu/~brill/Papers/encysbs.pdf
Chatfield, C. (2001). Time-series forecasting (1st ed.). CRC Press.
Dickey, D. A., & Fuller, W. A. (1979). Distribution of the Estimators for Autoregressive Time
Series with a Unit Root. Journal of the American Statistical Association, 74(366), 427-431.
Hyndman, R. J. (2001, May 25, 2001). Box-Jenkins Modeling. Retrieved from
http://www.statistical-solutions-software.com/BMDP-documents/BMDP-2T.pdf
Lawrence, J., & Pasternack, B. (2002). Applied Management Science: Modeling, Spreadsheet
Analysis, and Communication for Decision Making (2nd ed.). Hoboken, NJ: John Wiley &
Sons.
Nakamura, T., & Small, M. (2007). Testing for Random Walk. Physics Letters A, 362(2-3),
189-197.
Pankratz, A. (1983). Forecasting with Univariate Box-Jenkins Models (Vol. 3): Wiley Online
Library.
Spitzer, F. (2001). Principles of Random Walk (Second Ed.). New York: Springer Verlag.