Time Series Forecasting - Coursework Example

Time Series Forecasting Affiliation Number Introduction Time series and forecasting is an important area of research that has created interest in many researchers over a number of years. The major objective of time series modeling is to keenly collect and closely examine the past observations of a time series in order to come up with a suitable model that gives an inherent description of the series structure (Bowerman & Connell, 2009, P.109). This model is quite useful since it is used to generate future values for the series or simply making forecast. Therefore time series forecasting can be defined as the process of future prediction by gaining an understanding of the past. Time series and forecasting has been quite significant in practical areas such as finance, economics, agriculture, and science and engineering (Bowerman & Connell, 2009, P.109). It is important to show a lot of keenness when trying to fit a suitable model to the associated time series. Research has tried hard over the past few decades to develop effective models that can be used in improving the accuracy of forecasting. Consequently, there has been evolution of a number of important models of time series forecasting. This study aims at looking at the application of Time Series Forecasting and its relevance to the workplace. This research also focuses on the modeling of an application, the results and the knowledge learnt from the same (Bowerman & Connell, 2009, P.110). . One of the most significant time series that is being used frequently is the Autoregressive Integrated Moving Average (ARIMA) {6, 8, 21,23} model. The implementation of this model takes an assumption that the series being considered is linear and is in line with a specific statistical distribution like the normal distribution. The ARIMA model contains subclasses belonging to other models like the Autoregressive (AR) {6, 12, 23}.Autoregressive Moving Average {6, 21, 23}, and Moving Average {6, 23} models. In the case of Seasonal time series forecasting, there was a proposal of a very successful variant of the ARIMA model known as the seasonal ARMA(SARIMA) [3,6,23].ARIMA model is quite popular because of its ability to represent a number of time series in a simple way including the underlying Box-Jenkins methodology[3,6,8,23] y optimize the process of model building (Bowerman & Connell, 2009, P.109). . Application of Time Series Forecasting Time –Critical Decision modeling and Analysis The ability to come up with a model and carrying out decision modeling and analysis is an important aspect of several applications in the real world that range from medical care applications to military command and control systems. One of the major important characteristics of being a high profile manager is to have successful personal leadership and the ability to model your leadership skills for the employees in the company (Weigend 2014, P.57).Most management decisions are usually based on forecasts. In most cases, decisions become operation at a certain time in the future therefore this requires forecasts of future states and conditions. In any organization, forecasts are continually needed in some departments. For instance, many inventory management systems are required to cater for uncertain market demand. These systems contain inventory parameters that give estimates about the demand and provide forecasts on error distributions. The examination of forecasting and inventory control is done independently. Forecasting models are very important to decision-makers. The process of decision-making usually uses the modeling to carry out an investigation on the possible impacts associated with various courses of actions in a retrospective way. Time series forecasting is also an important in modeling financial decisions in a process known as financial modeling. An important aspect of financial planning is the ability to build models that show the interrelationships of financial data. Models that show the characteristic of correlation or regression between a number of variables can be quite useful in improving the process of financial decision making (Weigend 2014, P.60). Time series forecasting can also be used in business decision making. For example, it is useful in understanding the future of business behavior. By having an observation of data over a specific time period, it is easy for understand the changes that have occurred in the past and what is likely to happen in the future. Time series is also essential in to plan future operations. One of the major capabilities of a time series is the ability to predict an unknown value of the series. For decisions related with capital investment, decisions that are associated with inventory and production are some of the example of planning of future operations (Weigend 2014, P.61). The technology can also be useful in evaluating current business activities. In this, the actual performance of a business activity is compared with the expected performance and the reason for the variation is analysed.For example, if the expected number of sales for 2014 were 30 kirk trousers and the actual number of sales were only 25, one can try to find out the reason behind the decline in achievement. Concepts of Time Series Modeling. A time series is termed as a set of data points that can be measured over specific time intervals. Mathematically it can be described as a group of vectors x(t) where t =0,1,2…… and t is used to represent the time elapsed[21,23,31].x(t) is taken as a random variable. The measurements that are made during a particular event in a time series are usually organized in a chronological order (Weigend 2014, P.64). A time series which consists of records of a single variable is referred to as a univariate.On the other hand, if it contains records of a number of variables, it is termed to as a multivariate. Usually a time series can be discrete or continuous. In the case of a continuous time series, one makes observations at every time instance. Discrete time series on the other side observations are usually measured at discrete points of time. For instance, reading of temperature values can be taken as a continuous time series. Company production and the population of a particular region can be represented in discrete time series. Components of a time series There are four major components of a time series. These include: Trend This is a characteristic of a time series that makes it either to increase, decrease or can be stagnant for a long period of time. Therefore trend can be described as long term movement in a time series. An example is the growth of a population or the number of buildings in region. Seasonal variations These are used to describe fluctuations that occur within a specific time period during the season. For example the number of ice-cream sales increase in summer while the number of woolen clothes sales increase in summer. Seasonal variation is quite significant for manufacturers and business men for coming up with appropriate future plans for their businesses structure (Bowerman & Connell, 2009, P.118). Cyclical Variation-this is used to describe the medium-term changes that occur in a time series. The changes are due to circumstances which normally recur in cycles. The cycle durations goes for a longer time period, like two or even more years. Example to illustrate these is financial and economic time series that portray some form of cyclonical variation. An example of this is a business cycle which contains four phases that is prosperity, decline, depression and recovery structure (Bowerman & Connell, 2009, P.119). Irregular variations-these are usually due to influences or factor that cannot be predicted. The influences do not occur in a regular manner thus do not have a specific pattern. These variations may be as a result of factor such as earthquakes, war, and revolution and may others. Random fluctuations cannot be measured by any statistical technique. Time series Application Modeling Application modeling in a time series is achieved through the use of time series data. Time series data can be defined as a specific volume of data that can be used to predict or forecast the future behavior of a certain phenomenon such as the changes in the future market, environmental conditions, health trends and many others. One o example of an application forecasting model if the financial modeling discussed below: Inventory Application modeling If in case the demand forecasted for a row material in the process of manufacturing for the start of the next 12 time intervals is Period 1 2 3 4 5 6 6 8 9 10 11 12 Demand 200 150 100 50 50 100 150 200 200 250 300 250 The cost of ordering is $500, the unit price being $50 while the cost of holding is $1 per unit period. The major questions that are common in the management of general inventory include: what the order quantity should be? And at what time the orders should be placed. The table below shows the silver-Meal computations. Period Demand Lot QTY Holding Cost Lot Cost Mean Cost First Buy 1 200 200 0 500 500 2 150 350 150 650 325 3 100 450 150+2(100)=350 850 283 4 50 500 150+200+3(50)=500 1000 250 5 50 550 150+200+150+4(50)=700 1200 240 6 100 650 15+200+150+200+5(100)=1200 1700 283 Second Buy 6 100 100 0 500 500 7 150 250 150 650 325 8 200 450 150+2(200)=550 1050 350 Third Buy 8 200 200 0 500 500 9 200 400 200 700 350 10 250 650 200 + 2(250)=700 1200 400 Fourth Buy 10 250 250 0 500 500 11 300 550 300 800 400 12 250 800 300+2(250)=800 1300 433 Fifth Buy 12 250 250 0 500 500 Solution Summary Period Demand Order QTY Holding $ ordering $ Period Cost 1 200 550 350 500 850 2 150 0 200 0 200 3 100 0 100 0 100 4 50 0 50 0 50 5 50 0 0 0 0 6 100 250 150 500 650 7 150 0 0 0 0 8 200 400 200 500 700 9 200 0 0 0 0 10 250 550 300 500 800 11 300 0 0 0 0 12 250 250 0 500 500 Total 2000 2000 1350 2500 3850 In this case optimal solutions are used in trading off ordering and holding costs in the time periods which are based on the certainty of the demand schedule. Practically, the procedure is rerun monthly, while adding a new month to the end and eliminating the old month. Only the latest orders are placed. Conclusion Time series forecasting is an area that is growing very fast in the field of research .Its application on various field such as business can go a long way to improve business decision making and processes in organizations. References Bowerman, B. L., & OConnell, R. T. (2009). Time series and forecasting. North Scituate, Mass.: Duxbury Press. Weigend, A. S. (2014). Time series prediction: forecasting the future and understanding the past. Santa Fe Institute Studies in the Sciences of Complexity. Read More