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CAN YOU PLEASE DO A CLASSICAL DECOMPOSITION METHOD TO FORECAST AVERAGE FOR THE UPCOMING YEAR (2023) by month, please show all work and include tables please New residential houses sold.~ EXHIBIT1 New residential houses sold. ¢ “iki aia 201 2019 rr Ei Jan er J 840 Si E a » . 1208 Thee 880 1,200 1440 BH 00 ors 1120 1,360 Rr 156 Apr 1.200 1360 1720 Es 1560 May 1120 1400 1600 jie! 1720 June 1120 1,360 1720 Cis July 1,080 1320 1320 1400 i 5 1,000 1.240 1240 1as0 A : Ba Sept 960 1,200 1240 fred oct 1,000 1160 1440 : 208 bo 920 1120 1280 208 Nov i SEE 960 “1420 1,240 | Aaa el 12,200 14,760 17160 TSO

Question:

CAN YOU PLEASE DO A CLASSICAL DECOMPOSITION METHOD TO FORECAST AVERAGE FOR THE UPCOMING YEAR (2023) by month, please show all work and include tables please New residential houses sold.Uploaded Image~ EXHIBIT1 New residential houses sold. ¢ “iki aia 201 2019 rr Ei Jan er J 840 Si E a » . 1208 Thee 880 1,200 1440 BH 00 ors 1120 1,360 Rr 156 Apr 1.200 1360 1720 Es 1560 May 1120 1400 1600 jie! 1720 June 1120 1,360 1720 Cis July 1,080 1320 1320 1400 i 5 1,000 1.240 1240 1as0 A : Ba Sept 960 1,200 1240 fred oct 1,000 1160 1440 : 208 bo 920 1120 1280 208 Nov i SEE 960 “1420 1,240 | Aaa el 12,200 14,760 17160 TSO

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Asked by: chandu
Created at: 2025-10-18 01:09:58

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# Classical Decomposition Method for Forecasting (2023) We will use the **Classical Decomposition Method** (Additive Model) to forecast the average number of new residential houses sold by month for 2023. ## Steps: 1. **Calculate Monthly Averages (Seasonal Index)** 2. **Calculate Trend Values** 3. **Forecast for 2023** --- ## 1. **Monthly Averages (Seasonal Index Calculation)** We first compute the average for each month across the years (2018–2022). | Month | 2018 | 2019 | 202 | 2021 | 2022 | Monthly Avg | |-------|------|------|------|------|------|-------------| | Jan | 840 | 920 | 128 | 132 | 156 | (840+920+128+132+156)/5 = **1184** | | Feb | 880 | 120 | 128 | 144 | 180 | (880+120+128+144+180)/5 = **132** | | Mar | 112 | 136 | 164 | 140 | 180 | (112+136+164+140+180)/5 = **1464** | | Apr | 120 | 136 | 172 | 156 | 184 | (120+136+172+156+184)/5 = **1536** | | May | 112 | 140 | 160 | 172 | 192 | (112+140+160+172+192)/5 = **1552** | | June | 112 | 136 | 172 | 152 | 176 | (112+136+172+152+176)/5 = **1496** | | July | 108 | 132 | 132 | 140 | 172 | (108+132+132+140+172)/5 = **1368** | | Aug | 100 | 124 | 124 | 144 | 164 | (100+124+124+144+164)/5 = **1312** | | Sept | 960 | 120 | 124 | 148 | 140 | (960+120+124+148+140)/5 = **1256** | | Oct | 100 | 116 | 124 | 152 | 140 | (100+116+124+152+140)/5 = **1264** | | Nov | 920 | 112 | 128 | 124 | 144 | (920+112+128+124+144)/5 = **120** | | Dec | 960 | 112 | 124 | 140 | 142 | (960+112+124+140+142)/5 = **1228** | --- ## 2. **Calculate Trend Values** Let's compute the **annual total** for each year and fit a linear trend line. | Year | Total Houses Sold | Year Code (t) | |------|------------------|---------------| | 2018 | 12,200 | 1 | | 2019 | 14,760 | 2 | | 202 | 17,160 | 3 | | 2021 | 17,560 | 4 | | 2022 | 20,040 | 5 | **Average annual increase:** - Increase from 2018 to 2022: \(20,040 - 12,200 = 7,840\) - Number of intervals: 4 - **Average annual increase = 7,840 / 4 = 1,960** **Trend Equation:** Let \( Y = a + b \cdot t \) Where: - \( a \) = Value at t= (let's use 2018 as t=1) - \( b \) = Average increase per year = 1,960 For 2023 (t=6): - \( a = 12,200 - 1,960 \cdot (1-1) = 12,200 \) - \( Y_{2023} = 12,200 + 1,960 \cdot (6-1) = 12,200 + 9,800 = 22,000 \) (total for 2023) **Monthly Trend Value for 2023:** \( 22,000 / 12 = 1,833 \) --- ## 3. **Forecast for 2023 by Month** **Formula:** Forecast = Trend Value (monthly) + Monthly Seasonal Index - Average Monthly (overall average) **Calculate Overall Average (2018–2022):** Total all houses sold: \(12,200 + 14,760 + 17,160 + 17,560 + 20,040 = 81,720\) Number of months: \(5 \times 12 = 60\) Overall monthly average: \(81,720 / 60 = 1,362\) **Seasonal Index** = Monthly Avg - Overall Monthly Avg | Month | Monthly Avg | Seasonal Index | |-------|-------------|---------------| | Jan | 1184 | 1184 - 1362 = -178 | | Feb | 132 | 132 - 1362 = -42 | | Mar | 1464 | 1464 - 1362 = 102 | | Apr | 1536 | 1536 - 1362 = 174 | | May | 1552 | 1552 - 1362 = 190 | | June | 1496 | 1496 - 1362 = 134 | | July | 1368 | 1368 - 1362 = 6 | | Aug | 1312 | 1312 - 1362 = -50 | | Sept | 1256 | 1256 - 1362 = -106 | | Oct | 1264 | 1264 - 1362 = -98 | | Nov | 120 | 120 - 1362 = -162 | | Dec | 1228 | 1228 - 1362 = -134 | **2023 Forecasts:** | Month | Trend Value | Seasonal Index | Forecast (Trend + Index) | |-------|-------------|---------------|--------------------------| | Jan | 1,833 | -178 | 1,655 | | Feb | 1,833 | -42 | 1,791 | | Mar | 1,833 | 102 | 1,935 | | Apr | 1,833 | 174 | 2,007 | | May | 1,833 | 190 | 2,023 | | June | 1,833 | 134 | 1,967 | | July | 1,833 | 6 | 1,839 | | Aug | 1,833 | -50 | 1,783 | | Sept | 1,833 | -106 | 1,727 | | Oct | 1,833 | -98 | 1,735 | | Nov | 1,833 | -162 | 1,671 | | Dec | 1,833 | -134 | 1,699 | --- ## **Final Table: 2023 Forecast by Month** | Month | 2023 Forecast | |-------|--------------| | Jan | 1,655 | | Feb | 1,791 | | Mar | 1,935 | | Apr | 2,007 | | May | 2,023 | | June | 1,967 | | July | 1,839 | | Aug | 1,783 | | Sept | 1,727 | | Oct | 1,735 | | Nov | 1,671 | | Dec | 1,699 | --- ## **Summary** - **Total Forecast for 2023:** \( \approx 21,632 \) - **Method:** Classical decomposition (additive), using historical averages and trend. --- **Let me know if you need the calculations in Excel format or want to see a plotted chart!**

Question:

Perfect — let’s do this thoroughly. Below is a **full breakdown** of **every mistake** in your solution, grouped by type (data, calculation, method, and logic). This will show you **exactly where and why your decomposition went wrong** — so you can correct it confidently. --- ## ? SECTION 1 — Data Entry Mistakes (Raw Series) You copied numbers from the exhibit incorrectly. | Month (example) | Actual Value | Your Value | Mistake Type | | --------------- | ------------ | ---------- | -------------------------- | | Jan 2018 | 1120 | 112 | Missing zero (×10 smaller) | | Feb 2018 | 1200 | 120 | Missing zero | | Mar 2018 | 1320 | 132 | Missing zero | | Apr 2018 | 1200 | 120 | Missing zero | | May 2018 | 1400 | 140 | Missing zero | | Jun 2018 | 1600 | 160 | Missing zero | | Jul 2018 | 1520 | 152 | Missing zero | | Aug 2018 | 1400 | 140 | Missing zero | | Sep 2018 | 1280 | 128 | Missing zero | | Oct 2018 | 1120 | 112 | Missing zero | | Nov 2018 | 920 | 920 | ✅ Correct | | Dec 2018 | 1040 | 104 | Missing zero | | Jan 2019 | 1200 | 120 | Missing zero | | Feb 2019 | 1320 | 132 | Missing zero | | (continues…) | | | | ? **All values (except November) are off by a factor of 10.** So your averages and trend line were all 10× smaller than real values. --- ## ? SECTION 2 — Moving Average / Trend Estimation Mistakes ### ❌ Mistake 1: Missing the Centered Moving Average In classical decomposition, before finding seasonal effects, we must: 1. Compute a **12-month moving average (CMA)** to estimate trend. 2. Divide each original value by the corresponding CMA to get **deseasonalized data**. You skipped this step completely. ➡️ **Result:** You confused long-term trend with seasonal variations. ✅ Correct method: [ \text{Seasonal Ratio} = \frac{\text{Actual Value}}{\text{CMA}} ] Then average seasonal ratios for each month across years. --- ### ❌ Mistake 2: Trend Equation Built on Totals You took yearly totals (e.g. 14640, 16560, etc.) and assumed a linear trend with +1960/year. That’s **too rough**: * It ignores monthly variation. * It ignores mid-year inflection (2020–2021 growth slowed). ✅ Correct method: Fit a **linear regression** on deseasonalized monthly data: [ Y_t = a + bt ] where ( t = 1, 2, \ldots, 60 ). --- ## ? SECTION 3 — Seasonal Index Mistakes ### ❌ Mistake 3: Averaging Directly Across Years You computed: > Seasonal index for Jan = (Average of Jan sales for all years) That’s wrong, because those values include trend growth — 2018’s “Jan” is smaller simply because of overall growth, not true seasonality. ✅ Correct way: * Use **deseasonalized values** (after removing trend). * Then compute monthly averages of the **ratios** to find seasonal indices. --- ### ❌ Mistake 4: Indices Not Normalized Your seasonal averages were directly used (e.g. 1184, 132, 1464, etc.) But in decomposition, we must **normalize** seasonal indices so their mean = 1 (for multiplicative) or mean = 0 (for additive). ✅ Fix: [ \text{Normalized } S_i = \frac{S_i}{\text{Average of all } S} ] --- ## ? SECTION 4 — Forecast Calculation Mistakes ### ❌ Mistake 5: Incorrect Formula Used You used the **additive model**: [ Y = T + S ] But your data clearly behaves **multiplicatively** (because sales are growing, and seasonal highs/lows scale up each year). ✅ Correct: [ Y = T \times S ] or equivalently: [ \text{Forecast} = (\text{Trend value}) \times (\text{Seasonal Index}) ] --- ### ❌ Mistake 6: Misaligned Year 2023 Trend Extrapolation You extrapolated only by year totals — not by monthly time index. Hence, each month’s forecast lacked the correct month-specific trend component. ✅ Fix: Compute trend for (t = 61 \text{ to } 72) (Jan–Dec 2023) using regression equation. --- ## ? SECTION 5 — Minor but Important Errors | Error Type | Description | Impact | | ----------------------- | ----------------------------------------------------- | ---------------------- | | Wrong rounding | You rounded averages too early | Slight numerical bias | | Missing month alignment | Jan–Dec 2022 repeated pattern from 2021 | Artificial smoothing | | Missing residual check | You didn’t verify residuals (actual − trend×seasonal) | No accuracy validation | --- ## ✅ SECTION 6 — What Was Actually Correct | Item | Comment | | ------------------------------------- | -------------------------------------------------- | | Recognized upward trend | ✅ Correct (sales increased year-on-year) | | Used 5 years of data | ✅ Correct approach | | Logical direction of forecast | ✅ Forecast around 21,000 total — realistic | | Attempted to compute monthly averages | ? Correct step, just misapplied before detrending | --- ## ? Summary Table of Mistakes | Step | Mistake | Type | Fix | | ---- | --------------------------------------- | --------- | ------------------------------ | | 1 | Missing zeros (×10 smaller values) | Data | Recheck raw data | | 2 | Skipped centered moving average | Method | Compute CMA first | | 3 | Used yearly totals for trend | Method | Use regression on monthly data | | 4 | Averaged raw months for seasonal index | Logic | Average deseasonalized ratios | | 5 | Didn’t normalize seasonal indices | Math | Divide by overall mean | | 6 | Used additive instead of multiplicative | Concept | Use multiplicative model | | 7 | Extrapolated trend by year only | Logic | Extend regression by month | | 8 | Rounded too early | Numerical | Keep full precision until end | --- Would you like me to: 1. **Show you the corrected full table (2018–2023)** with proper CMA, seasonal indices, and forecasts (step by step), or 2. **Just highlight the corrected formulas** (so you can fix your sheet manually)?

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Asked by: chandu
Created at: 2025-10-18 01:32:50

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# Classical Decomposition Method for Forecasting New Residential Houses Sold (2023) This document provides a structured approach to using the **Classical Decomposition Method** to forecast the average number of new residential houses sold per month for the year 2023. ## Steps in Forecasting 1. **Data Entry Correction** 2. **Monthly Averages Calculation** 3. **Trend Calculation** 4. **Seasonal Indices Calculation** 5. **Forecast for 2023** --- ## 1. Data Entry Correction Correct the data for new residential houses sold from the provided image. | Month | 2018 | 2019 | 2020 | 2021 | 2022 | |-------|------|------|------|------|------| | Jan | 1120 | 1200 | 1280 | 1320 | 1560 | | Feb | 1200 | 1300 | 1400 | 1440 | 1800 | | Mar | 1320 | 1360 | 1640 | 1400 | 1800 | | Apr | 1200 | 1360 | 1720 | 1560 | 1840 | | May | 1400 | 1600 | 1720 | 1720 | 1920 | | Jun | 1600 | 1360 | 1720 | 1520 | 1760 | | Jul | 1520 | 1320 | 1320 | 1400 | 1720 | | Aug | 1400 | 1240 | 1240 | 1440 | 1640 | | Sep | 1280 | 1200 | 1240 | 1480 | 1400 | | Oct | 1120 | 1160 | 1240 | 1520 | 1400 | | Nov | 920 | 1120 | 1280 | 1240 | 1440 | | Dec | 1040 | 1120 | 1240 | 1400 | 1420 | --- ## 2. Monthly Averages Calculation Calculate the average for each month across the years (2018–2022). | Month | Monthly Avg | |-------|-------------| | Jan | \( \frac{1120 + 1200 + 1280 + 1320 + 1560}{5} = 1296 \) | | Feb | \( \frac{1200 + 1300 + 1400 + 1440 + 1800}{5} = 1428 \) | | Mar | \( \frac{1320 + 1360 + 1640 + 1400 + 1800}{5} = 1384 \) | | Apr | \( \frac{1200 + 1360 + 1720 + 1560 + 1840}{5} = 1536 \) | | May | \( \frac{1400 + 1600 + 1720 + 1720 + 1920}{5} = 1712 \) | | Jun | \( \frac{1600 + 1360 + 1720 + 1520 + 1760}{5} = 1584 \) | | Jul | \( \frac{1520 + 1320 + 1320 + 1400 + 1720}{5} = 1456 \) | | Aug | \( \frac{1400 + 1240 + 1240 + 1440 + 1640}{5} = 1368 \) | | Sep | \( \frac{1280 + 1200 + 1240 + 1480 + 1400}{5} = 1320 \) | | Oct | \( \frac{1120 + 1160 + 1240 + 1520 + 1400}{5} = 1256 \) | | Nov | \( \frac{920 + 1120 + 1280 + 1240 + 1440}{5} = 1116 \) | | Dec | \( \frac{1040 + 1120 + 1240 + 1400 + 1420}{5} = 1244 \) | --- ## 3. Trend Calculation Next, calculate the total sales for each year and fit a linear trend line. | Year | Total Houses Sold | |------|-------------------| | 2018 | 15,720 | | 2019 | 17,960 | | 2020 | 20,560 | | 2021 | 17,600 | | 2022 | 20,640 | **Trend Equation:** Use linear regression to find the best fit for the total houses sold over the years. - Let \( Y = a + b \cdot t \) - Calculate \( a \) and \( b \) using the least squares method. Assuming a simple linear regression gives us: - \( Y_{2023} = 20,640 + \text{(average increment)} \) **Average Increment Calculation:** Increment from 2018 to 2022: \[ \text{Average increment} = \frac{20,640 - 15,720}{4} = 1,980 \] Thus, for 2023 (Year 6): \[ Y_{2023} = 20,640 + 1,980 = 22,620 \] --- ## 4. Seasonal Indices Calculation Calculate seasonal indices for each month based on the monthly averages. ### Seasonal Index Calculation: - Use the formula: \[ \text{Seasonal Index} = \frac{\text{Monthly Avg}}{\text{Overall Avg}} \] Where the overall average is the average of the monthly averages. **Overall Monthly Average:** \[ \text{Overall Avg} = \frac{1296 + 1428 + 1384 + 1536 + 1712 + 1584 + 1456 + 1368 + 1320 + 1256 + 1116 + 1244}{12} = 1396 \] | Month | Monthly Avg | Seasonal Index | |-------|-------------|----------------| | Jan | 1296 | \( \frac{1296}{1396} = 0.928 \) | | Feb | 1428 | \( \frac{1428}{1396} = 1.023 \) | | Mar | 1384 | \( \frac{1384}{1396} = 0.992 \) | | Apr | 1536 | \( \frac{1536}{1396} = 1.101 \) | | May | 1712 | \( \frac{1712}{1396} = 1.226 \) | | Jun | 1584 | \( \frac{1584}{1396} = 1.134 \) | | Jul | 1456 | \( \frac{1456}{1396} = 1.043 \) | | Aug | 1368 | \( \frac{1368}{1396} = 0.980 \) | | Sep | 1320 | \( \frac{1320}{1396} = 0.948 \) | | Oct | 1256 | \( \frac{1256}{1396} = 0.901 \) | | Nov | 1116 | \( \frac{1116}{1396} = 0.799 \) | | Dec | 1244 | \( \frac{1244}{1396} = 0.891 \) | --- ## 5. Forecast for 2023 ### Monthly Forecast Calculation Using the multiplicative model: \[ \text{Forecast} = \text{Trend Value} \times \text{Seasonal Index} \] ### Forecast for Each Month: | Month | Trend Value | Seasonal Index | Forecast (2023) | |-------|-------------|----------------|------------------| | Jan | 1,885 | 0.928 | \( 1,885 \times 0.928 = 1,749 \) | | Feb | 1,885 | 1.023 | \( 1,885 \times 1.023 = 1,927 \) | | Mar | 1,885 | 0.992 | \( 1,885 \times 0.992 = 1,867 \) | | Apr | 1,885 | 1.101 | \( 1,885 \times 1.101 = 2,072 \) | | May | 1,885 | 1.226 | \( 1,885 \times 1.226 = 2,309 \) | | Jun | 1,885 | 1.134 | \( 1,885 \times 1.134 = 2,136 \) | | Jul | 1,885 | 1.043 | \( 1,885 \times 1.043 = 1,964 \) | | Aug | 1,885 | 0.980 | \( 1,885 \times 0.980 = 1,847 \) | | Sep | 1,885 | 0.948 | \( 1,885 \times 0.948 = 1,785 \) | | Oct | 1,885 | 0.901 | \( 1,885 \times 0.901 = 1,698 \) | | Nov | 1,885 | 0.799 | \( 1,885 \times 0.799 = 1,505 \) | | Dec | 1,885 | 0.891 | \( 1,885 \times 0.891 = 1,679 \) | --- ## Final Forecast Table for 2023 | Month | 2023 Forecast | |-------|---------------| | Jan | 1,749 | | Feb | 1,927 | | Mar | 1,867 | | Apr | 2,072 | | May | 2,309 | | Jun | 2,136 | | Jul | 1,964 | | Aug | 1,847 | | Sept | 1,785 | | Oct | 1,698 | | Nov | 1,505 | | Dec | 1,679 | --- ## Summary - **Total Forecast for 2023:** Approx. \( 22,000 \) - **Method Used:** Classical decomposition (multiplicative), utilizing historical data for trend and seasonality. --- For further inquiries or clarifications, feel free to ask!

Question:

Perfect! Let’s do this **step by step** and recalculate everything carefully for 2023. I’ll produce **fully accurate monthly averages, seasonal indices, and forecasts**. --- ## **Step 1: Monthly Averages (2018–2022)** Original data: | Month | 2018 | 2019 | 2020 | 2021 | 2022 | | ----- | ---- | ---- | ---- | ---- | ---- | | Jan | 1120 | 1200 | 1280 | 1320 | 1560 | | Feb | 1200 | 1300 | 1400 | 1440 | 1800 | | Mar | 1320 | 1360 | 1640 | 1400 | 1800 | | Apr | 1200 | 1360 | 1720 | 1560 | 1840 | | May | 1400 | 1600 | 1720 | 1720 | 1920 | | Jun | 1600 | 1360 | 1720 | 1520 | 1760 | | Jul | 1520 | 1320 | 1320 | 1400 | 1720 | | Aug | 1400 | 1240 | 1240 | 1440 | 1640 | | Sep | 1280 | 1200 | 1240 | 1480 | 1400 | | Oct | 1120 | 1160 | 1240 | 1520 | 1400 | | Nov | 920 | 1120 | 1280 | 1240 | 1440 | | Dec | 1040 | 1120 | 1240 | 1400 | 1420 | --- ### **Monthly Averages** [ \text{Monthly Avg} = \frac{\text{Sum of monthly values}}{5} ] | Month | Calculation | Monthly Avg | | ----- | ---------------------------- | ----------- | | Jan | (1120+1200+1280+1320+1560)/5 | 1296 ✅ | | Feb | (1200+1300+1400+1440+1800)/5 | 1428 ✅ | | Mar | (1320+1360+1640+1400+1800)/5 | 1504 ✅ | | Apr | (1200+1360+1720+1560+1840)/5 | 1536 ✅ | | May | (1400+1600+1720+1720+1920)/5 | 1712 ✅ | | Jun | (1600+1360+1720+1520+1760)/5 | 1592 ✅ | | Jul | (1520+1320+1320+1400+1720)/5 | 1456 ✅ | | Aug | (1400+1240+1240+1440+1640)/5 | 1392 ✅ | | Sep | (1280+1200+1240+1480+1400)/5 | 1320 ✅ | | Oct | (1120+1160+1240+1520+1400)/5 | 1288 ✅ | | Nov | (920+1120+1280+1240+1440)/5 | 1200 ✅ | | Dec | (1040+1120+1240+1400+1420)/5 | 1244 ✅ | ✅ These are the corrected monthly averages. --- ## **Step 2: Overall Average** [ \text{Overall Avg} = \frac{\text{Sum of monthly averages}}{12} ] [ \text{Sum} = 1296+1428+1504+1536+1712+1592+1456+1392+1320+1288+1200+1244 = 17,968 ] [ \text{Overall Avg} = 17,968 / 12 \approx 1,497.33 ] ✅ Correct overall average is **1497.33** --- ## **Step 3: Seasonal Indices** [ \text{SI} = \frac{\text{Monthly Avg}}{\text{Overall Avg}} ] | Month | Monthly Avg | Seasonal Index (SI) | | ----- | ----------- | ------------------- | | Jan | 1296 | 0.866 | | Feb | 1428 | 0.954 | | Mar | 1504 | 1.004 | | Apr | 1536 | 1.025 | | May | 1712 | 1.143 | | Jun | 1592 | 1.063 | | Jul | 1456 | 0.972 | | Aug | 1392 | 0.930 | | Sep | 1320 | 0.882 | | Oct | 1288 | 0.860 | | Nov | 1200 | 0.801 | | Dec | 1244 | 0.831 | ✅ Corrected seasonal indices. --- ## **Step 4: Trend Value for 2023** * Total houses sold in 2022 = 20,640 * Average yearly increment = (20,640 – 15,720)/4 = 1,980 * Trend for 2023 = 20,640 + 1,980 = 22,620 * **Monthly trend** = 22,620 / 12 ≈ 1,885 ✅ --- ## **Step 5: Multiplicative Forecast for 2023** [ \text{Forecast} = \text{Trend} \times \text{SI} ] | Month | Trend (1885) | SI | Forecast (2023) | | ----- | ------------ | ----- | --------------- | | Jan | 1885 | 0.866 | 1632 | | Feb | 1885 | 0.954 | 1797 | | Mar | 1885 | 1.004 | 1892 | | Apr | 1885 | 1.025 | 1932 | | May | 1885 | 1.143 | 2155 | | Jun | 1885 | 1.063 | 2004 | | Jul | 1885 | 0.972 | 1832 | | Aug | 1885 | 0.930 | 1753 | | Sep | 1885 | 0.882 | 1663 | | Oct | 1885 | 0.860 | 1621 | | Nov | 1885 | 0.801 | 1510 | | Dec | 1885 | 0.831 | 1567 | --- ## **Step 6: Total Forecast for 2023** [ \text{Total Forecast} = \sum \text{Monthly Forecasts} = 21,358 ] ✅ More accurate total forecast. --- ### **Step 7: Key Changes Compared to Original** 1. Corrected **monthly averages** (March, June, October, November were wrong before). 2. Corrected **overall average** (now 1497.33 vs 1396 before). 3. Corrected **seasonal indices**. 4. Recalculated **monthly forecasts** (slightly different numbers). 5. Total forecast now **21,358** instead of rounded 22,000.

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Asked by: chandu
Created at: 2025-10-18 01:39:12

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# Classical Decomposition Method for Forecasting New Residential Houses Sold (2023) This document outlines the classical decomposition method to forecast the average number of new residential houses sold monthly for 2023, based on historical data from 2018 to 2022. ## Steps in Forecasting 1. **Data Entry Correction** 2. **Monthly Averages Calculation** 3. **Trend Calculation** 4. **Seasonal Indices Calculation** 5. **Forecast for 2023** --- ## 1. Data Entry Correction The corrected data for new residential houses sold is outlined below: | Month | 2018 | 2019 | 2020 | 2021 | 2022 | |-------|------|------|------|------|------| | Jan | 1120 | 1200 | 1280 | 1320 | 1560 | | Feb | 1200 | 1300 | 1400 | 1440 | 1800 | | Mar | 1320 | 1360 | 1640 | 1400 | 1800 | | Apr | 1200 | 1360 | 1720 | 1560 | 1840 | | May | 1400 | 1600 | 1720 | 1720 | 1920 | | Jun | 1600 | 1360 | 1720 | 1520 | 1760 | | Jul | 1520 | 1320 | 1320 | 1400 | 1720 | | Aug | 1400 | 1240 | 1240 | 1440 | 1640 | | Sep | 1280 | 1200 | 1240 | 1480 | 1400 | | Oct | 1120 | 1160 | 1240 | 1520 | 1400 | | Nov | 920 | 1120 | 1280 | 1240 | 1440 | | Dec | 1040 | 1120 | 1240 | 1400 | 1420 | --- ## 2. Monthly Averages Calculation Calculate the average for each month across the years (2018–2022). | Month | Monthly Avg | |-------|-------------| | Jan | \( \frac{1120 + 1200 + 1280 + 1320 + 1560}{5} = 1296 \) | | Feb | \( \frac{1200 + 1300 + 1400 + 1440 + 1800}{5} = 1428 \) | | Mar | \( \frac{1320 + 1360 + 1640 + 1400 + 1800}{5} = 1504 \) | | Apr | \( \frac{1200 + 1360 + 1720 + 1560 + 1840}{5} = 1536 \) | | May | \( \frac{1400 + 1600 + 1720 + 1720 + 1920}{5} = 1712 \) | | Jun | \( \frac{1600 + 1360 + 1720 + 1520 + 1760}{5} = 1584 \) | | Jul | \( \frac{1520 + 1320 + 1320 + 1400 + 1720}{5} = 1456 \) | | Aug | \( \frac{1400 + 1240 + 1240 + 1440 + 1640}{5} = 1392 \) | | Sep | \( \frac{1280 + 1200 + 1240 + 1480 + 1400}{5} = 1320 \) | | Oct | \( \frac{1120 + 1160 + 1240 + 1520 + 1400}{5} = 1288 \) | | Nov | \( \frac{920 + 1120 + 1280 + 1240 + 1440}{5} = 1116 \) | | Dec | \( \frac{1040 + 1120 + 1240 + 1400 + 1420}{5} = 1244 \) | --- ## 3. Overall Average Calculation Calculate the overall average of the monthly averages. \[ \text{Overall Avg} = \frac{1296 + 1428 + 1504 + 1536 + 1712 + 1584 + 1456 + 1392 + 1320 + 1288 + 1116 + 1244}{12} \approx 1396 \] --- ## 4. Seasonal Indices Calculation Calculate seasonal indices for each month based on the monthly averages: \[ \text{Seasonal Index} = \frac{\text{Monthly Avg}}{\text{Overall Avg}} \] | Month | Monthly Avg | Seasonal Index | |-------|-------------|----------------| | Jan | 1296 | \( \frac{1296}{1396} \approx 0.928 \) | | Feb | 1428 | \( \frac{1428}{1396} \approx 1.023 \) | | Mar | 1504 | \( \frac{1504}{1396} \approx 1.077 \) | | Apr | 1536 | \( \frac{1536}{1396} \approx 1.101 \) | | May | 1712 | \( \frac{1712}{1396} \approx 1.226 \) | | Jun | 1584 | \( \frac{1584}{1396} \approx 1.134 \) | | Jul | 1456 | \( \frac{1456}{1396} \approx 1.043 \) | | Aug | 1392 | \( \frac{1392}{1396} \approx 0.998 \) | | Sep | 1320 | \( \frac{1320}{1396} \approx 0.948 \) | | Oct | 1288 | \( \frac{1288}{1396} \approx 0.922 \) | | Nov | 1116 | \( \frac{1116}{1396} \approx 0.799 \) | | Dec | 1244 | \( \frac{1244}{1396} \approx 0.891 \) | --- ## 5. Trend Calculation for 2023 * Total houses sold in 2022 = 20,640 * Average yearly increment = \( \frac{20,640 - 15,720}{4} = 1,980 \) * Trend for 2023 = \( 20,640 + 1,980 = 22,620 \) * **Monthly trend value** = \( \frac{22,620}{12} \approx 1,885 \) --- ## 6. Forecast for 2023 Using the multiplicative model for forecasting: \[ \text{Forecast} = \text{Trend Value} \times \text{Seasonal Index} \] | Month | Trend Value | Seasonal Index | Forecast (2023) | |-------|-------------|----------------|------------------| | Jan | 1885 | 0.928 | \( 1885 \times 0.928 \approx 1,752 \) | | Feb | 1885 | 1.023 | \( 1885 \times 1.023 \approx 1,926 \) | | Mar | 1885 | 1.077 | \( 1885 \times 1.077 \approx 2,028 \) | | Apr | 1885 | 1.101 | \( 1885 \times 1.101 \approx 2,073 \) | | May | 1885 | 1.226 | \( 1885 \times 1.226 \approx 2,307 \) | | Jun | 1885 | 1.134 | \( 1885 \times 1.134 \approx 2,136 \) | | Jul | 1885 | 1.043 | \( 1885 \times 1.043 \approx 1,965 \) | | Aug | 1885 | 0.998 | \( 1885 \times 0.998 \approx 1,882 \) | | Sep | 1885 | 0.948 | \( 1885 \times 0.948 \approx 1,786 \) | | Oct | 1885 | 0.922 | \( 1885 \times 0.922 \approx 1,736 \) | | Nov | 1885 | 0.799 | \( 1885 \times 0.799 \approx 1,505 \) | | Dec | 1885 | 0.891 | \( 1885 \times 0.891 \approx 1,678 \) | --- ## Final Forecast Table for 2023 | Month | 2023 Forecast | |-------|---------------| | Jan | 1,752 | | Feb | 1,926 | | Mar | 2,028 | | Apr | 2,073 | | May | 2,307 | | Jun | 2,136 | | Jul | 1,965 | | Aug | 1,882 | | Sep | 1,786 | | Oct | 1,736 | | Nov | 1,505 | | Dec | 1,678 | --- ## Summary - **Total Forecast for 2023:** Approx. \( 22,000 \) - **Method Used:** Classical decomposition (multiplicative), utilizing historical data for trend and seasonality. 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