Time Series - 1 Method of Least Squares - Fitting of Linear Trend - Odd number of years
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- Опубликовано: 11 сен 2024
- #Statistics #Time #Series #Business #Forecasting #Linear #Trend #Values #LeastSquares #Fitting #Odd
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 Linear Trend
Let the straight line trend between the given time series values (y) and time (x) be given by the standard equation: y = a + bx
Then for any given time ‘x’ the estimated value of ye as given by the equation is ye = a + bx
The following two normal equations are used for estimating 'a' and 'b'.
Σy = na + bΣx
Σxy = aΣx + bΣx^2
When Odd No. of Years, [X = (Year - Origin) / Interval]
Case
Given below are the figures of sales (in '000 units) of a certain shop. Fit a straight line by the method of least square and show the estimate for the year 2017:
Year: 2010 2011 2012 2013 2014 2015 2016
Sales: 125 128 133 135 140 141 143
Time Series, Linear Trend, 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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Happy to here that you could perform well in your exams and cleared it. Don’t forget to recommend my channel/lectures to others. It would be a great gesture and that will also benefit to the other students. Keep learning and growing. Stay Blessed.
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Welcome...
Keep watching, keep learning...
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And also visit, subscribe and recommend my channel ruclips.net/channel/UCqedkv6AYxh3hk99EPtGlmQ to the others...
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I hv understood the least square method.
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Sir please telugu lo explain cheyara...I am telugu medium student sir.....pls I request u to sir....your explanation is superb sir,please........sir
Thank you for the appreciation... I am happy to know about the faith you have in my teaching.... but the only problem is; I have to learn Telugu up to the level of fluency for that purpose and starting to learn a new language will distract me from my this work, which I think, at this stage, will not be good for all of us... I have already started bilingual lectures, explaining new cases in English and Hindi, which may be useful to you... :)
thanks sir...
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Sir one question ,if the estimation for 2017 needed ,then n( no of years ) becomes even ( earlier it was odd so base year was differently taken{the middle one} ) ,in this case will the base year remain same as in earlier case where n was odd ????
Just to clarify... Thank u...
Not to worry... this game of 'odd number of years' and 'even number of years' etc stands only for the time when we are going to fit the trend for the available time series and "not at all for getting the trend value or forecast from the fitted trend" :)
@@PUAARAcademy thanks sir.
hlo sirrr ur teaching way is superb 👌👌👌 sir aap compiund intrest or annuity wale chaptrs ki bhi vedios upload krdoo plzzz
Yes, I will be uploading a series of lectures on all such chapters very soon... :)
hmmm thnkuu very much sirrr
I am finding difficult to calculate X2 pls assist.
Hi sir, Do you have videos on ARIMA model or State space method? if you have send me link. your lectures are very easily understandable. thanks. reply me plz
@Prashant Puaar
I meant how did u get 9, 4 etc
What if there where even number of years what will be the origin
I have explained everything but in different lectures taking suitable cases/examples/problems... please visit and subscribe my RUclips channel where there are playlists on many topics/chapters of different subjects, which you will always find very useful. Also suggest this to others... Thanks... :)
It can be trend analysis na?? similar ryt trend and least square???
Answer plz
I have exam
Ryt now
The estimated (y^) values of the periods considered for fitting the equations are also known as 'trend values', which we can use for further analysis like short term fluctuations, seasonal fluctuations, seasonal indices etc...
@@PUAARAcademy , but is it similar??🙄
Actually there is no specific chapter named "Trend Analysis". If you express any time series data in the form of percentages of the previous value(s), then also it is termed as 'trend analysis'
What will we do when the no of years is even
I have discussed everything but in different lectures taking suitable new problem/case/question...
The '1' in Time Series - 1 (and FTM in all my lectures) stands for the lecture number on the chapter/topic ('Time Series' here) and that directly means that there are also other lectures on the same topic/chapter, which obviously will cover new problems/cases/questions with new points... Many teachers like to discuss all the points while solving/discussing one (and only) problem in the classroom, but that itself is the reason that more and more students now like to learn from our lectures HERE against the formal classroom... I try to keep this thing in my mind while presenting any topic/chapter here and prefer to discuss different important points taking different problems/cases/questions to solve and explain... I hope you and all other students could understand this thing and take little effort to appreciate and making others aware of it ...:)
Make in hindhi
Sir covid mein apna lheyal rkhna
Thanks for caring... You too take care and don't forget to get vaccinated on time...:)
@@PUAARAcademy yes sir definitely
The short-term trends are components of both major and intermediate trends. As a short time trader I am with Trade12 broker with whom I have the most fluent trading platform, technical errors free environment and smart bridge technology.
sir,statistical quantity control mAth lecture
Yes, it's in the pipeline... very soon I'll be here with that... :)
Sir Hindi may vedio bano
Moving average???
There is a playlist on this chapter, and other playlists on many other chapters/topics on my channel, where there are lectures explaining everything... :)
@@PUAARAcademy ,this one is not moving average ryt?
Yes, it is not... You can find it from the title itself...
@@PUAARAcademy ok
@@PUAARAcademy , I need some help in rank correct, regression analysis, regression Line,index number....I have exam ..
Super sir thank u so much🙏
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