Time series analysis to predict the future values when we have seasonal variations.

1. GLOBAL TRAINING AND
CONSULTING HOUSE

2. Advanced Budgeting and
Forecasting
GLOBAL TRAINING AND
CONSULTING HOUSE
Presented by Ajendra Selvaratnam
October 16- 27, 2023

3. Session Objectives
• Time Series Analysis for Accurate Forecasting
• Seasonality and Trend Analysis
• Regression Analysis for Predictive Modeling
• Combining Forecasting Methods for Robust Predictions

4. Think a minute
Let’s say you are running a business selling winter coats. Would you like
to diversify your business by starting an ice-cream manufacturing
business?

5. How are we going to predict the sales for next
January?

6. Time Series Analysis - Components
A data set of observations recorded in equal intervals over a period of
time (CIMA).
A time series is a sequence of data points that occur in successive order
over some period of time (Investopedia).
Key Terms:
Trend (T): The underlying general movement over time.
Seasonal Variation (SV): A regular variation within the data related to
calendar or season. Eg: Weather seasons.
Cyclical variation (C): A variation within the data related to a cyclical
pattern. Eg: Economic cycle.
Residual variation (R): Irregular or unpredictable changes in the data.
Eg: Impact of cyclone or war.

7. Models used in Time Series Analysis
Addictive Model: It assumes that all the components are independent
of each other.
TS = T+SV+C+R
Multiplicative Model: It assumes that the components are dependent
of each other.
TS = T*SV*C*R

8. Example - 01
Weeks Monday Tuesday Wednesday Thursday Friday
Week 01 160 174 164 180 150
Week 02 180 190 186 204 170
Week 03 210 224 206 232 190
Week 04 240 254 236 262 210
The total sales of Anbu plc for each day of a month is given below in “$
millions”.
Identify the trend and calculate the average seasonal variation using
addictive model.

9. 100
120
140
160
180
200
220
240
260
280
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
1 2 3 4
Sales

10. Example 01 – Calculation of Trend
Weeks Days Sales
1 Monday 160
Tuesday 174
Wednesday 164
Thursday 180
Friday 150
2 Monday 180
Tuesday 190
Wednesday 186
Thursday 204
Friday 170
3 Monday 210
Tuesday 224
Wednesday 206
Thursday 232
Friday 190
4 Monday 240
Tuesday 254
Wednesday 236
Thursday 262
Friday 210

11. Example 01 – Calculation of Trend (Cont….)
Weeks Days Sales Moving Average
1 Monday 160
Tuesday 174
Wednesday 164 165.6
Thursday 180 169.6
Friday 150 172.8
2 Monday 180 177.2
Tuesday 190 182
Wednesday 186 186
Thursday 204 192
Friday 170 198.8
3 Monday 210 202.8
Tuesday 224 208.4
Wednesday 206 212.4
Thursday 232 218.4
Friday 190 224.4
4 Monday 240 230.4
Tuesday 254 236.4
Wednesday 236 240.4
Thursday 262 240.5
Friday 210 236

12. 100
120
140
160
180
200
220
240
260
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
1 2 3 4
Sales
$Million
Days
Seasonal Sales with the trend

13. Let’s predict the sales for the fifth week
Weeks Days Sales Moving Average Seasonal Variance
1 Monday 160
=Sales – Moving
Average
Tuesday 174
Wednesday 164 165.6 -1.60
Thursday 180 169.6 10.40
Friday 150 172.8 -22.80
2 Monday 180 177.2 2.80
Tuesday 190 182 8.00
Wednesday 186 186 0.00
Thursday 204 192 12.00
Friday 170 198.8 -28.80
3 Monday 210 202.8 7.20
Tuesday 224 208.4 15.60
Wednesday 206 212.4 -6.40
Thursday 232 218.4 13.60
Friday 190 224.4 -34.40
4 Monday 240 230.4 9.60
Tuesday 254 236.4 17.60
Wednesday 236 240.4 -4.40
Thursday 262 240.5 21.50
Friday 210 236 -26.00

14. Let’s calculate the average seasonal variance
Column1 Week 01 Week 02 Week 03 Week 04 Average
Monday 2.80 7.20 9.60 6.5333
Tuesday 8.00 15.60 17.60 13.7333
Wednesday -1.60 0.00 -6.40 -4.40 -3.1000
Thursday 10.40 12.00 13.60 21.50 14.3750
Friday -22.80 -28.80 -34.40 -26.00 -28.0000
Days Monday Tuesday Wednesday Thursday Friday
Total
Difference
Average
Difference
Average 6.5333 13.7333 -3.1000 14.3750 -28.0000 3.5417 0.708333333
Add Average
Difference 0.708333333 0.708333333 0.708333333 0.708333333 0.708333333
5.8250 13.0250 -3.8083 13.6667 -28.7083 0.0000

15. Let’s predict the sales for the fifth week
Weeks Days Sales Moving Average
Seasonal
Variance
Average Seasonal
Variance
1 Monday 160 5.8250
Tuesday 174 13.0250
Wednesday 164 165.6 -1.60 -3.8083
Thursday 180 169.6 10.40 13.6667
Friday 150 172.8 -22.80 -28.7083
2 Monday 180 177.2 2.80 5.8250
Tuesday 190 182 8.00 13.0250
Wednesday 186 186 0.00 -3.8083
Thursday 204 192 12.00 13.6667
Friday 170 198.8 -28.80 -28.7083
3 Monday 210 202.8 7.20 5.8250
Tuesday 224 208.4 15.60 13.0250
Wednesday 206 212.4 -6.40 -3.8083
Thursday 232 218.4 13.60 13.6667
Friday 190 224.4 -34.40 -28.7083
4 Monday 240 230.4 9.60 5.8250
Tuesday 254 236.4 17.60 13.0250
Wednesday 236 240.4 -4.40 -3.8083
Thursday 262 240.5 21.50 13.6667
Friday 210 236 -26.00 -28.7083

16. Let’s predict the sales for the fifth week
Predicting the trend = (236-165.6)/18 = 3.91
Expected Sales = Trend + Seasonal Variance
Weeks Days
Moving Average
(Trend)
Seasonal Variance Expected Sales
5 Monday =236+3.91 5.8250
Tuesday =(236+3.91)+3.91 13.0250
Wednesday =236+3.91*3 -3.8083
Thursday 236+3.91*4 13.6667
Friday 236+3.91*5 -28.7083

17. Let’s predict the sales for the fifth week
Weeks Days
Moving Average
(Trend)
Seasonal Variance Expected Sales
5 Monday 239.91 5.83 245.74
Tuesday 243.82 13.03 256.85
Wednesday 247.73 -3.81 243.93
Thursday 251.64 13.67 265.31
Friday 255.56 -28.71 226.85

18. Multiplicative Model

19. Example - 02
Weeks Monday Tuesday Wednesday Thursday Friday
Week 01 160 174 164 180 150
Week 02 180 190 186 204 170
Week 03 210 224 206 232 190
Week 04 240 254 236 262 210
The total sales of Anbu plc for each day of a month is given below in “$
millions”.
Identify the trend and calculate the average seasonal variation using
multiplicative model.

20. 100
120
140
160
180
200
220
240
260
280
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
1 2 3 4
Sales

21. Example 01 – Calculation of Trend
Weeks Days Sales
1 Monday 160
Tuesday 174
Wednesday 164
Thursday 180
Friday 150
2 Monday 180
Tuesday 190
Wednesday 186
Thursday 204
Friday 170
3 Monday 210
Tuesday 224
Wednesday 206
Thursday 232
Friday 190
4 Monday 240
Tuesday 254
Wednesday 236
Thursday 262
Friday 210

22. Example 01 – Calculation of Trend (Cont….)
Weeks Days Sales Moving Average
1 Monday 160
Tuesday 174
Wednesday 164 165.6
Thursday 180 169.6
Friday 150 172.8
2 Monday 180 177.2
Tuesday 190 182
Wednesday 186 186
Thursday 204 192
Friday 170 198.8
3 Monday 210 202.8
Tuesday 224 208.4
Wednesday 206 212.4
Thursday 232 218.4
Friday 190 224.4
4 Monday 240 230.4
Tuesday 254 236.4
Wednesday 236 240.4
Thursday 262 240.5
Friday 210 236

23. 100
120
140
160
180
200
220
240
260
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
1 2 3 4
Sales
$Million
Days
Seasonal Sales with the trend

24. Let’s predict the sales for the fifth week
Weeks Days Sales Moving Average Seasonal Variance
1 Monday 160
=Sales/Moving
Average
Tuesday 174
Wednesday 164 165.6 0.99
Thursday 180 169.6 1.06
Friday 150 172.8 0.87
2 Monday 180 177.2 1.02
Tuesday 190 182 1.04
Wednesday 186 186 1.00
Thursday 204 192 1.06
Friday 170 198.8 0.86
3 Monday 210 202.8 1.04
Tuesday 224 208.4 1.07
Wednesday 206 212.4 0.97
Thursday 232 218.4 1.06
Friday 190 224.4 0.85
4 Monday 240 230.4 1.04
Tuesday 254 236.4 1.07
Wednesday 236 240.4 0.98
Thursday 262 240.5 1.09
Friday 210 236 0.89

25. Let’s calculate the average seasonal variance
Week 01 Week 02 Week 03 Week 04 Average
Monday 1.02 1.04 1.04 1.0310
Tuesday 1.04 1.07 1.07 0.0644
Wednesday 0.99 1.00 0.97 0.98 0.9855
Thursday 1.06 1.06 1.06 1.09 1.0689
Friday 0.87 0.86 0.85 0.89 0.8649
Days Monday Tueday Wednesday Thursday Friday
Total
Differen
ce
Average
Difference
Average 1.0310 1.0644 0.9855 1.0689 0.8649 5.0147 0.0029378
Reduce Average
Difference 0.00294 0.00294 0.00294 0.00294 0.00294
1.0281 1.0615 0.9825 1.0659 0.8620 5.0000

26. Let’s predict the sales for the fifth week
Weeks Days Sales Moving Average Seasonal Variance
Average Seasonal
Variance
1 Monday 160 1.0281
Tuesday 174 1.0615
Wednesday 164 165.6 0.99 0.9825
Thursday 180 169.6 1.06 1.0659
Friday 150 172.8 0.87 0.8620
2 Monday 180 177.2 1.02 1.0281
Tuesday 190 182 1.04 1.0615
Wednesday 186 186 1.00 0.9825
Thursday 204 192 1.06 1.0659
Friday 170 198.8 0.86 0.8620
3 Monday 210 202.8 1.04 1.0281
Tuesday 224 208.4 1.07 1.0615
Wednesday 206 212.4 0.97 0.9825
Thursday 232 218.4 1.06 1.0659
Friday 190 224.4 0.85 0.8620
4 Monday 240 230.4 1.04 1.0281
Tuesday 254 236.4 1.07 1.0615
Wednesday 236 240.4 0.98 0.9825
Thursday 262 240.5 1.09 1.0659
Friday 210 236 0.89 0.8620

27. Regression Analysis

28. Example 03
The total production cost of Ko plc for its three products are given below for last two
years. Forecast the total production cost when A = 800, B = 600 and C = 1000 units.
Months Product A (Units) Product B (Units) Product C (Units) Total Cost ($)
1 644 900 289 52,770
2 117 163 684 24,070
3 339 216 865 31,910
4 815 974 742 62,940
5 138 634 844 40,220
6 989 601 334 51,150
7 680 714 985 54,870
8 282 289 542 29,730
9 954 268 851 45,630
10 731 603 893 51,640
11 226 155 533 24,500
12 378 404 691 36,590
13 251 407 750 34,730
14 283 810 786 47,820
15 242 974 743 51,490
16 175 395 479 30,140
17 308 495 832 39,330
18 436 998 190 50,560
19 151 534 396 33,000
20 755 245 119 33,640
21 602 762 974 54,640
22 442 259 748 34,090
23 532 669 260 43,310
24 318 540 831 40,870

29. Let’s do it with me in the class

30. Time Series Analysis with
Regression Analysis
Multiplicative Model

31. Example 03
Years Quarter 01 Quarter 02 Quarter 03 Quarter 04
2020 160 174 164 180
2021 180 190 186 204
2022 210 224 206 232
The total sales of Anbu plc for each qua of 2020-2022 is given below in
“$ millions”.
Calculate the sales for the first quarter of 2023 using Excel.

32. Let’s do it with me in the class

33. Activity 01
The ice cream sales (units in thousands) of Arasan limited for the years
2021 to 2023 are given below.
Estimate the sales for the seasons in 2024 using,
1. Addictive model
2. Multiplicative model
Summer Spring Autumn Winter
2021 500 450 300 120
2022 600 550 400 220
2023 700 650 500 320

34. Activity 02
The daily production level (units in thousands) of the employees of
Alfred manufacturers for the month of January is given below.
Estimate the sales for the days in February using multiplicative model
and regression analysis in Excel.
Monday Tuesday Wednesday Thursday Friday
Week 01 1200 1100 1130 1080 780
Week 02 1600 1500 1530 1480 1180
Week 03 2000 1900 1930 1880 1580
Week 04 1800 1700 1730 1680 1380

35. Activity 03
The total production cost and the total revenue details of Hassan
traders for the last 24 months is given in the next slide.
Calculate the total profit when the production level of,
A = 1300
B = 800
C = 1180

36. Months Product A (Units) Product B (Units) Product C (Units) Total Cost ($) Total Revenue ($)
1 765 360 1115 47,250 54,075
2 929 382 699 47,030 53,635
3 680 671 474 48,470 54,350
4 1054 862 336 60,300 71,140
5 1005 840 488 60,180 71,070
6 927 712 715 57,050 67,015
7 1155 1155 866 76,410 93,840
8 634 623 527 46,640 51,845
9 659 963 786 59,930 70,080
10 1082 962 769 68,190 82,475
11 666 834 983 58,170 68,085
12 1183 445 844 55,450 65,950
13 925 460 756 49,860 57,490
14 1031 1165 1161 77,180 94,945
15 1167 353 339 47,320 54,215
16 1051 422 610 49,780 57,560
17 413 505 1196 45,370 50,530
18 526 521 1129 47,440 53,555
19 498 641 636 45,550 50,120
20 848 428 727 47,070 53,465
21 476 1013 421 54,120 61,115
22 1182 537 322 52,970 61,770
23 953 902 1007 66,190 79,775
24 949 455 644 49,070 56,330

37. Summary
We learnt to,
• Use the time series analysis to forecast the future estimates using addictive
and multiplicative models.
• Understand the terms trend, seasonal variations, cyclical variation and
random variation.
• Use regression analysis for predictive modeling.
• combine forecasting methods for robust predictions.

38. Thank you
Contact me: growingajay@gmail.com