Time Series - 6 Non-linear Trend - Second Degree Parabola - Quadratic Method
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- Опубликовано: 27 окт 2024
- #Statistics #Time #Series #Business #Forecasting #NonLinear #Trend #Values #SecondDegree #Parabola #Quadratic
Definitions
“A time series may be defined as a sequence of values of same variable corresponding to successive points in time.” - W. Z. Hersch
“A time series may be defined as a sequence of repeated measurement of a variable made periodically through time.” - Cecil H. Mayers
Analysis of Time Series
“The main object of analyzing time series is to understand, interpret and evaluate changes in economic phenomena in the hope of more correctly anticipating the course of future events.” - Hersch
A time series is a dynamic distribution, which reveals a good deal of variations over time. Statistical methods are, therefore, required to analyze various types of movements in a time series. There may be cyclical variations in general business activity and there may be short duration seasonal variations. There are also some accidental and random variables. The primary purpose of the analysis of time series is to discover and measure all such types of variations, which characterize a time series.
Time series analysis means analyzing the historical patterns of the variable that have occurred in past as a means of predicting the future value of the variable. It helps to identify and explain the following:
(i) Any regular or systematic variation in the series of data which is due to seasonality- the ‘seasonal’
(ii) Cyclical patterns.
(iii) Trends in the data.
(iv) Growth rates of these trends.
This method can be useful when no major environmental changes are expected and it does highlight seasonal variations in sales and consumer demand. However, time series analysis is limited when organizations face volatile environments.
Components of Time series -
The time series are classified into four basic types of variations which are analyzed below:
T = Trend
S = Seasonal variations
C = Cyclic variations
I = Irregular fluctuations.
This composite series is symbolized by the following general terms: O = T x S x C x I
Where
O = Original data
T = Trend
S = Seasonal variations
C = Cyclic variations
I = Irregular components.
This Multiplicative model is to be used when S, C, and I are given in percentages. If, however, their true (absolute) values are known the model takes the additive form i.e., O=T+C+S+I.
Algebraic Method For Finding Trend (Method of curve fitting by the principle of Least Squares)
Fitting of Non-linear Trend
Second Degree parabola / Quadratic Method
Standard Equation
y = a + bx + cx^2
The following three normal equations are used for estimating 'a', 'b' and 'C'.
Normal Equations
(i) Σy = na + bΣx + cΣx^2
(ii) Σxy = nΣx + bΣx2 + cΣx^3
(iii) Σx^2y = aΣx^2 + bΣx^3 + cΣx^4
Case
Fit a parabola y = a + bx + cx^2 to this data. Estimate the price of the commodity for the year 2017
Year 2011 2012 2013 2014 2015 2016
Price 100 107 128 140 181 299
Time Series, Non-linear Trend, Second Degree Parabola, Method of Least Squares, Statistics, MBA, MCA, BE, CA, CS, CWA, CMA, CPA, CFA, BBA, BCom, MCom, BTech, MTech, CAIIB, FIII, Graduation, Post Graduation, BSc, MSc, BA, MA, Diploma, Production, Finance, Management, Commerce, Engineering , Grade-11, Grade- 12
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thanks sir I am a engineering student and you save me. in my 6th sem
Thanks Mwalimu for that explanation
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Sir you are a life saver. Very easy to understand.
Thanks alot sir, Your lectures were of great use to me....
Amazingly explained!
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when finding x why did you divide it by half instead of 1 because the interval from each year is 1
How do you get the trend values estimate when the years are in range of ten 1901 to 1911 upto 1971 then you asked trend value of 1973
Sir you are really good..thanks for helping us out...
Thanku so much sir
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@@PUAARAcademy welcome sir ji
Sir thank u very much it is very helpful for me in my BSC part 1 paper 👍👍
Thank u sir, it was so much helpful.
Sir agr ic me hum orgin at begining ly skty hn?? Ans py jo farak pary gaa but correct e hoga na?? Trend values same hn naa?
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Sir nice teaching but little slow sir thank u
can you plz tell how to evaluate the same where months are there instead of years?? please tell me soon
Kasina madam bag
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HOW TO FIND OUT THE INTERVAL??
Interval means the gap between two consecutive periods/years in the data, which is one here. Hence, the value of the denominator in the formula is "half of one = 1/2 = 0.5".Total number of years are six here that means this data having even number of periods...
Sir what happened when interval between two years is not same ?