TIME SERIES ANALYSIS THE BEST EXAMPLE

good day I would like to welcome you to the lecture on time series analysis time series analysis is one of the easier sections for those you were starting your MBA in quantitative methods this lesson is more inclined towards those learners that are doing quantitative methods in management colleges in South Africa but can be adapted to other countries as well the section on time series analysis is quite an easy section once you master the concept we're going to be looking at an example and working through the example this should ensure that you understand the concept of time series analysis when I come across time series analysis the question that I'm going to be dealing with here is one that has appeared in some examinations and passed let's go for it it says the table below gives the quarterly sales figures in millions of rands off a retail giant for the years 2008 to 2010 normally a question like this you'll be given a table 2008 2009 2010 the quarterly sales figures are given the year is broken up into four quadrants namely quarter one quarter two quarter three and quarter four and this at the bottom here will be the sales figures for example the sales figures for quarter three for the year 2009 is sixty two and obviously sixty two million the questions using the ratio two moving average method calculate seasonally adjusted indices for each water question number to obtain a regression trendline representing the above data and normally the third question obtain a seasonally adjusted trend estimate for the fourth quarter of 2011 what you notice a is 2011 does not here in our given information so we are going to estimate or basically make a prediction based on our calculation of time series now in order to begin I'm going to go back to the table Quarter 120 of 2008 quarter to thirty quarter three of 2008 thirty-nine quarter for 2008 60 I am simply going to transcribe these figures on to my next table and the next table is something that you have to know I have the time period with my years I have the quarter quarter one quarter two quarter three quarter 4 2009 beginning with the quarter's again and 2010 beginning with the four quarter's again at the top my time period the quarters I have something called an Xcode I would explain that later on this is why which means the given information for qma stands for the four quarter moving average then I have something called the centered average and lastly percentage of average you need to understand and learn this off now let's go filling in my information my Xcode Xcode is simply allocating a code for each quarter so to make it easier quarter one I'll give it Xcode one two three four now be careful down here I'm dealing with an Xcode so this becomes a coding of 5 6 7 8 9 10 11 and 12 so I've given my codings from one right up to 12 then the next thing someone might question is why do I have these two together the last two together but gaps in between now for simplicity and if you are answering onto an answer sheet it is much much easier to leave it exactly as it is it works out perfectly when you're calculating the rest of the aspects so get into the habit of using quarter one and quarter to two and the last two quarter's together leave a gap between each water after that next I'm going to put down the values as given to me in the question twenty thirty thirty nine and on it or not these values that I'm plugging in here are directly from the question so if I go down to twenty ten quarter four I have 95 2009 quarter two it is 51 so so far I've done nothing major I've simply put in what I have been given and I've allocated my X codes when you allocate the X codes an important point is if you are given another method called the zero average that's something totally different and that we will deal with Italian aspect if you had not asked anything about zero average then you simply go ahead n and work from one to twelve next step I'm going to work with the four quarter moving average four quarter moving average now as the name suggests it's an average I'm dealing with the four quarter's which meaning I would take four quarter's at a time and calculate the average of four quarter's at a time now watch this I deal with first quarter second quarter third quarter and the fourth quarter I add them up 20 plus 30 plus thirty nine plus 60 you can do that on your calculators once I get an answer I take whatever answer I get here and I divide it by four and if I divide that by four I should get the answer that comes up here which is 37 comma to five now watch where the answer came up it came up in the gap all I did once again once I added for averages or the four quarter's I divided by four and I got the four quarter moving average how's that that's quite easy now if I want to go to the next portion watch what I do here just take that out for now I don't want that to come out there let's go to the next one if I want to get the next value remember I have to add up for take that out so now to add up the four quarter's I take the 30 plus the 39 plus the 60 plus the 40 I add these up and once I add them up and if I divide by four it will give me the answer that goes into the slaughter house that guy's quite easy now go to the next one let me change the color of the Pandya just to make it a bit easier for me to be able to locate the different ones let's go with that now remember I've died out word that is over if I want the next value I take the next four and the next four is the 39 plus the 60 plus the 40 plus the 51 I add those four and if I divide them by four it gives me the answer that comes in there and that answer is forty seven comma five and guys I go on and on and on with the same process let me do one more then you can get an understanding of why I am let's change the point to option again in color okay let me go with a highlighter for now the next thing remember finished off with that I go the next for the next four is the 60 last the 40 last the 51 plus the 62 when I add those up and divide by four it should give me the answer that comes up here alternatively what you can do if I were to fill this space go in between add the two up the two bottom divided by four and you get to the next answer and all that happens after those guys is I work on and on and on let's just get rid of all this demarcations so watch the next four if I want this value it's that Plus that Plus that Plus that I get that value how's that guys if I want this value it's 51 plus 62 plus 81 plus 50 divided by 4 I get that value if I want the next one yeah wonderful something India I go with the 62 plus the 81 plus the 50 plus the 64 divided by 4 if I want this value is equal to up to around 81 plus 50 plus 64 plus 74 and I get that value now watch what happens here if I won this one it's 50 plus 64 plus 74 + 94 divided by 4 and I get that answer can I go any further I want to go to more quadrature I cannot I need to have all four quarters so that's the position where I stop so the 4 quarter moving average was quite simple let's go over to the next one the center the average centered means in the center - so all I'm going to do is I'm going to repeat the procedure that I did here except I'm going to use the four quarter moving average to generate the answer for this column down here but I'm going to now work in twos so I am going to go ahead here let's go back to the pen and work 37 plus 42 comma 2 5 I get an answer I divide that answer by 2 and that will give me the answer and the answer is 39 comma seven five now you would notice I'm going to be doing the exact same thing over and over again if I want the next answer which should come in this gap here I take the 42 comma five plus that divided by 2 and I get that answer what about the next one gasps I'll take that one last that one divided by two and that gives me 50 comma 3 let me do one more for the next one I take that one Plus that one 53 combo 2 5 + 58 comma 5 make sure you get your answer you divide it by two and that gives you the next answer and I can go on and on and on and on and this is the point that I saw how's that guys quite easy and the last one is very very easy for me to get the percentage average I simply work with not original y-value I work with the calculated centered average and I work out the percentage of these two which means I take the 39 I divided by the 39 comma 7 5 and I multiply it by 100 and that will give me a percentage and the percentage that I get is 98 comma one one percent let me do one more if I want the percentage err I take the 60/40 four comma eight eight and remember guys multiply by 100 because you need it as a percentage what about the next one 40 divided by 50 comma 3 8 multiply by 100 and gives me seventy nine comma four percent I go to the next one and the next one and the next one and the next one and the last one is 64 divided by six to nine remember x and I get 92 comma 75% now please remember that have generated these answers for a reason I'm going to use them in my next step 2008 quarter three the percentage average is 98 comma 1 1 4 2008 what - for the percentage is 133 comma 7 percent and on and on and on the next thing that you would have to do is generate another table and this here deals with the year 2008 2009 2010 the quarter quarter one quarter two quarter three and quarter for these are the answers that I had in the previous table these answers here I have simply taken them and put them onto the table now guys unfortunately this is another table that you have to know off at the bottom this is the mean multiplied by the adjustment factor and finally the seasonal index let's go back to what has been given or what has been calculated and provided in this table for quarter one I've got two values quarter two I've got two values the mean what does the mean mean I like saying that what does the mean mean the mean is simply an average how do you calculate an average guys the mean we do it on yeah the mean is an average if I want to calculate the mean for quarter one I use 79 comma 4 + 76 comma zero five and I divided by two and that gives me the meat likewise I add this 2 divided by 2 I add those two divided by 2 I add those two values divided by 2 and I get the mean the next step is I need to add up all the mean values end up with the value down here and this value becomes 402 comma 2 percent which automatically is a problem 402 comma 2% because I'm dealing with the four quarter moving average four quarter's ideally I should end up here with four hundred percent nothing more nothing less now the question is how do I convert this 402 comma - how do I bring it to 400 per set and this is done by using something called the adjustment factor this formula is given to you in your formula sheets the adjustment factor is what I need the 400 over the value that I obtained and once I do 400 over 400 - comma - I get the adjustment factor of zero comma nine nine four five all I simply do is put in the adjustment factor and I'm going to multiply the mean by the adjustment factor the mean multiplied by the adjustment factor gives me the value for the seasonal index the mean multiplied by my adjustment factor it gives me the mean multiply multiply and when I add up all these values I should end up with four hundred percent that multiplied by that will give me four hundred percent guys please ensure that you have four hundred percent you might have to do some rounding of rules here in order to get this four hundred percent very very important and lastly I want you to remember this later I will show you why I want you to remember this portion let's go further I have now answered the first question to get the seasonal index let me move over now to the next question and the next question is the question where I need to get the change equation the trend equation is given by a simple equation y is equal to a plus BX if I have a scatterplot and I need the line of best fit I use regression analysis in order to get this now if I am dealing with this trendline I'm going to be dealing with the same thing I'm going to use regression analysis in order for me to get the gray irrigation line equation I need to get the value for B and I need to get the value for a let's start afloat how do I get the value for B turn to your formula sheets and the equation to calculate B is given yeah hey this seems like a very very long equation but it is not so B is equal to n is the sample size this Sigma stands for the sum of sum of x times y sum of X sum of Y sum of X all squared sum of x squared now I'll go further in terms of how I'm going to use this but for now this is the equation to calculate B the equation to calculate a is given as the senior formula sheets but I do not like to use this equation the reason I do not like to use it is if I have to look at this portion here what is that the sum of Y divided by n I've explained it previously the sum of Y divided by n is actually the mean so that can be written as the mean of Y likewise the sum of X divided by n that can be written as the mean of X so therefore I prefer using that equation and once I get this equation guys I now have my trend line equation how do I go about getting the value for B in the value of a I now go into another table that this may seem monotonous but this table gives me the trend line I start off by using my X code remember I deal deal with X code before one right up to 12 then I have my Y as from the original question as well these are my Y values coming down now how do I know that I need to put in here x times y in x squared very very easy I get this from the equation according to my equation I need to get the sum of X Y so it means I need to know x times y I also need to get here x squared and that is why I know I need x squared now remember guys this is X that is why in order for me to get X Y it means x x y 1 times 20 gives me a value of 22 times 20 sorry 2 times 30 is 60 3 times 39 is 170 I'm sure by now you get the picture of what I'm doing monotonous but at the same time guys you need to be accurate what about x squared self-explanatory this is X if I square that I get the value for you 1 squared is 1 2 squared is 4 3 squared is 9 4 squared is 16 and on and on and on until I come up with 12 squared which is 144 right at the bottom if I have to add up all these X values here i get the sum of x agreed and the sum of x is equal to 78 working with the 78 i can get the mean the mean of x is 78 divided by 12 which is equal to 6 comma 5 likewise these are wise if i go down and add up all the y-values i end up with the sum of Y if I divide by 12 because the sample size is 12 I get the mean of Y which is 55 comma 5 now what happens if I have to add up all these values now let's correct I get the sum of XY and the sum of XY is 5,000 n69 and lastly guys what about x squared if you have to add up all the x squared values coming down here i get the sum of x squared which is 650 so me to get the trend equation I'm simply going to use these values with the sample size which is 12 and I'm going to get the trendline equation I've calculated all of this from the previous table it seems long but once you get a hang of it guys it's very very easy okay chain equation y is equal to a plus BX that's we are heading the formula calculate B is s so what's the value in 12 the sum of XY the sum of X Y is this value minus the sum of X what's the sum of X 78 the sum of Y some of our is 0 6 6 6 n is 12 sub of x squared these are not the same the sum of x squared is 650 the sum of X all squared is the 78 all squared I simply plug the correct values into the equation using a calculator I get the value 5 comma 1 7 what about the value for a a is equal to the mean of Y minus B times the mean of X the mean of Y I've got it the mean of X I've got it the value for B I've got I simply calculate the value for a once I've got a and B I now end up with my trendline equation which is y is equal to 21 comma 9 plus 5 comma 1 7 X easy by now you should be smiling because these are marks in the bag let me go over now to the last question the last question says obtain a seasonally adjusted trend estimate for the fourth quarter of 2011 this question can be different they can ask you any quarter of let's say 2011 first second third or fourth quarter they could ask you any one of them they could ask you all four I will just simply do the fourth quarter but everything else will be the same my trend equation is y is equal to 21 combine 9 + 5 comma 1 7 and remember this was X where in the world did I get the 60 in front really very easy guys I've got my 3 years my X codes went right from 1 to 12 agreed and let us 2010 quarter for your 2011 quarter 1 is going to be number thirteen quarter two is going to be number fourteen quarter three is going to be number 15 and 44 is going to be Xcode which is 60 so dependent on which quarter they ask you you are going to substitute the correct Xcode in order to generate the value for y easy but I'm not complete there's one more step this is not the answer the value needs to be multiplied by the seasonal index of quarter four which is 132 comma 84% remember that star that I told you to remember down here the seasonal index the seasonal index for quarter four is 130 comma eight percent agreed so I have to multiply it by 100 that you come eight percent if I was dealing with quarter three it'll be this value if I was dealing with quarter two it will be that value and if I was dealing with quarter one it will be seventy seven comma three percent I simply take the 100 comma 62 I multiplied by 130 comma eight four percent which is 132 comma eight four is missing divided by 100 is going to say that that's percentage per one handled do what you do multiplied by 130 got my 84 and decide that is your answer it's one that you come by eight four percent meaning per 100 and that gives me my final answer which means the expected sales should be around hundred and thirty six million eight hundred and forty thousand rare and this should be a 25 mark question in the exams simple yet quite effective understand this example you can understand every example henceforth now this has been a lesson done by a TA consultants which is a consultancy in South Africa that deals with net training also MBA statistics training we can be contacted on oh eight three six five three eight five six eight as do lessons as well both in Durban and Johannesburg thank you for your time and if you can leave any comments it will be appreciated so that we can either enhance this video or provide more videos of the same quality thank you very much

Channel: Adhir Hurjunlal

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Length: 26min 4sec (1564 seconds)

Published: Wed Nov 27 2013