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Analysis of Time Series Forecastng

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Analysis of Time Series and Forecasting:

Analysis of Time Series and Forecasting Project By: Nivedita Mehta(Food Tech.) Priyal Mangla ( Instru .) Salma Firdaus Tanisha Gupta Sukriti Sacher Sanya Kumar BMS

Introduction:

Introduction Future prediction is always a matter of great concern in any organization. It is of great interest in almost every field such as economics, commerce, business, weather, stock market, sociology, biology, public health etc.

Time Series:

Time Series “A set of statistical observations arranged in chronological order” - Morris Hamburg

Why analyze Time Series?:

Why analyze Time Series? Main objectives Understanding past behavior : by looking at the series one can know the nature of the series which in turn helps in determining the general trend. Estimation and forecasting : forecast doesn’t tell what will happen in future but merely predicts what might happen in the future if the past trend continues.

Components of Time Series:

Components of Time Series A time series is obtained by measurement of variable over a period of time. Changes in value of this variable is attributed to four factors called components of Time Series. Secular Trend Seasonal Variations Cyclic Variations Irregular or Random Variations

Secular Trend:

Secular Trend Its long term movement of a time series The trend may be upward, downward or steady These factors aren't evident in short term but become obvious when summed up.

Seasonal variations:

Seasonal variations Complete within a period of one year. Its basically a movement that occurs with some degree of regularity within a definite period. happens because of climatic conditions, festivals and customs.

Cyclic variations:

Cyclic variations Wave like movements noticeable over extended period of time which repeat in cycles. Have a longer term than seasonal variations Called business cycles

PowerPoint Presentation:

A peak time, known as prosperity or boom, followed by decline also called recession, extends to low point or trough called depression followed by recovery, which leads to a new peak and the cycle begins again.

Irregular movements:

Irregular movements 2 types: Random and Episodic Random or Chance variations are present in everything that is real Episodic movements are variations that result from identifiable causes like labor strike, flood etc. These factors aren't under human control and might influence Time Series favorably or unfavorably.

Decomposition of Time Series:

Decomposition of Time Series Process of segregating each value of time series into its 4 components is called decomposition of time series. Each component is measured one by one and eliminated before other components are taken into consideration.

PowerPoint Presentation:

The four components form models that describe Time series: Additive Model : four components of time series are independent and additive Multiplicative Model : four components of time series are not independent and hence multiplicative.

Measurement of Trend:

Measurement of Trend Method of Least Squares…

Example: Computation of straight line trend:

Example: Computation of straight line trend Year (t) Production (y) x= t- origin x 2 xy Trend Values y= ax+b 2006 12 12-14= -2 4 -24 Explained In Upcoming Slides ! 2007 13 -1 1 -13 2008 14 0 0 0 2009 15 1 1 15 2010 22 2 4 44 2011 23 3 9 69 Total 99 3 19 91 Origin: Value of ‘c’ gives the value of variable in question at origin chosen. It’s the middle value. In above case origin is 2008.

Let’s Solve ! :

Let’s Solve ! Let the straight line trend be y Equations are: i.e. i.e. Solving above two equations a= 15.31 and b=2.37

PowerPoint Presentation:

Year (t) Production (y) X= t- origin x 2 xy Trend Values y= 15.31+ 2.37x 2006 12 2006-2008 = -2 4 -24 15.31+2.37(-2)= 10.57 2007 13 -1 1 -13 15.31+2.37(-1) = 12.94 2008 14 0 0 0 15.31+2.37(0)= 15.31 2009 15 1 1 15 15.31+2.37(1)= 17.68 2010 22 2 4 44 15.31+2.37(2)= 20.05 2011 23 3 9 69 15.31+2.37(3)= 22.42 Total 99 3 19 91

PowerPoint Presentation:

To predict production in year 2013 in previous example t= 2013 x= t-2008 = 2013-2008= 5 Put Y in equation of straight line trend y=15.31+2.37(5)= 27.16 tonnes

Conclusion:

Conclusion Time series data have a natural temporal ordering. This makes time series analysis distinct from other common data analysis problems. In this there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order) Time series analysis can be applied to real-valued, continuous data, discrete numeric data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the English language.

Thank You! :

T hank You !

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