## Forecasting Quantitative Time Series using statistical methods

Forecasting , or predicting is a vital tool in any decision making process. It uses vary from determining inventory requirements for local shop to estimating the annual sales of TV. The quality of forecasts management can be strongly related to the information that can be extracted and used from past data. Time series  analysis is one of the quantitative methods we can use to determine patterns in data collected over time. Time series analysis is used to detect patterns of change in statistical information over regular intervals of time.

## What is time series and forecasting ?

Forecasting is a very common technique and has become an integral part of every business decision and even in our lives. We try to forecast life decisions consciously or subconsciously to get the best possible outcome. It's a very important tool that can break or make any business today. Forecasting is the process of predicting future events based on old data. The old data is used in systematic in order to forecast future events. Forecasting is the estimation of the future that is not subject to subjective considerations. Forecasting technique is classified into two :

• Qualitative method

• Quantitative method

In a qualitative technique, we use the judgment of experts and develop some forecast. This method is generally used when the old data to the variable is not available.Whereas, In quantitative forecasting is used when:

(1)  Old information about the variable is available,

(2)  Information being used is quantified.

(3) We assume that the pattern observed would be similar to the old one.

Historically speaking, time series analysis has been almost for ages, and its proof can be seen in the area of astronomy where it was applied to investigate the changes of the planets and the sun in ancient times. Today, it is used in almost every field around us- business concerns to complex scientific study and research

## What are components in time series forecasting?

A time series, in general, is affected by four components. These components are Trend, Seasonal, Cyclical and Irregular components. Seasonal variation is a very important factor for any businessmen for making future plans. Decision makers study sales forecasts like they take decisions on capital needs, the size of the force, levels of inventory, the location of facilities, the amount of advertising, the impact of changes in prices, scheduling of production and many more.

A time series is a sequence of data points, typically over periodic times.Mathematically, it can be defined as a set of vectors

z(t), t = 0,1,2,3,4......

Where t represents the time elapsed.

z(t): random variable

1. TRENDS : These generally relate to long term changes whether linearly or non linearly in data. Like changes could be linear like price increase or decline in market share. The below example of a decreasing linear trend :

2. SEASONALITY  : These are periodic changes that get impacted on the particular time frame. There are repetitive variations in time-series which may occur due to buying patterns and social habits of the customers during a year.

3. REGULAR VARIATIONS:  These variations are due to fluctuations in data which are not being monitored or not detailed analysis is performed, which can be taken care of in order to have valid explanations for erratic fluctuations. Such fluctuations are due to a variety of factors which could be sudden weather changes or some clashes. As these variations are truly random so their occurrence in the future will have an impact on sales.

4. CYCLICAL VARIATIONS : These variations arises due to the phenomenon of business cycles. The business cycle refers to the periods of expansion followed by periods of contraction.The business cycle may vary yearly according to cyclic variations. The duration and the level of sales may vary depending on the nature of the business that are quite difficult to predict.

Considering these above components the effect can be calculated using two different types of models are generally used for a time series viz. Multiplicative and Additive models.

Multiplicative Model : Y(t) = t(t)× s(t)×c(t)× i(t)

Additive Model :  Y(t) =t(t) + s(t) + c(t) + i(t)

Y(t) = observation at time t

t(t) =the trend component

s(t) = the  seasonal component

c(t)= the cyclic component

i(t)=irregular component

In Multiplicative model assumes that the four components of  time series may or may not be independent and they might affect one another. In additive model we assume that all the four components are independent of each other.

What is the need of forecasting ?

1. Purpose – Any activity conceived in the present to deal with some possibility of gathering out of a circumstance or set of conditions set in the future. These future conditions offer a reason/focus to be accomplished in order to exploit or to limit the effect of  these future conditions. Therefore, poor forecasts may lead to poor planning, thereby increasing the operational cost of the company. Hence, it's important to forecast the future with the best ability, experience and Judgment.

2. Time – To get ready arrangement, to sort out assets for its usage, to execute; and complete the arrangement; all these need time as an asset. A few circumstances need next to no time, while some need quite a long time. Thusly, if future gauge is accessible ahead of time, proper activities can be arranged and executed in-time.

## STATISTICAL METHODS FOR FORECASTING :

1. ### Residual Method:-

 YEAR QUARTER1 QUARTER 2 QUARTER3 QUARTER4 TOTAL DEMAND 1 25 78 25 75 203 2 56 45 36 72 209 3 84 65 45 80 274 4 75 75 85 65 300 5 32 95 75 49 251 6 89 45 66 55 255

APPLICATIONS OF FORECASTING :

Estimating Economic Trends

With the conceivable exemption of offers determining, the most broad estimating exertion is dedicated to anticipate  financial patterns on a territorial, national, or even global level.

Estimating Staffing Needs

For monetarily created nations there is moving accentuation from assembling to administrations. Products are being delivered outside the nation (where work is part) and after that imported. Simultaneously, an expanding number of business firms are having some expertise in giving an administration or the like (e.g., travel, the travel industry, excitement, lawful guide, wellbeing administrations, monetary, instructive, plan, upkeep, and so on.). For such an organization gauging "deals" progresses toward becoming anticipating the interest for administrations, which at that point converts into determining staffing needs to give those administrations.

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