Q6
(a) Explain Box-Jenkins methodology to build ARIMA models. (15 marks) (b) Prepare the cost of living index for 2006 on the basis of 2005 from the above data by (i) aggregative method and (ii) method of weighted relatives and comment. (15 marks) (c) Explain price statistics relating to 'Price Quotations'. Elucidate publications of data concerning foreign trade of India. (20 marks)
हिंदी में प्रश्न पढ़ें
(a) अरीमा (ARIMA) निदर्शों को बनाने के लिए बाक्स-जेनकिंस विधि तंत्र की व्याख्या कीजिए। (15 अंक) (b) निम्नलिखित आंकड़ों से 2005 के आधार पर 2006 के लिए निर्वाह-सूचकांक तैयार कीजिए (i) सामुदायिक विधि द्वारा और (ii) भारित अनुपातों की विधि द्वारा, और अपनी टिप्पणी दीजिए। (15 अंक) (c) 'मूल्य कोटेशनों' से संबंधित मूल्य आंकड़े बताइए। भारत के विदेशी व्यापार के विषय में आंकड़ों के प्रकाशनों को स्पष्ट कीजिए। (20 अंक)
Directive word: Explain
This question asks you to explain. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.
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How this answer will be evaluated
Approach
The directive 'explain' demands clear exposition with logical flow and appropriate technical depth. Allocate approximately 30% time/words to part (a) on Box-Jenkins methodology, 30% to part (b) on index number calculations with explicit working, and 40% to part (c) covering price quotations and foreign trade publications. Structure: brief conceptual introduction for each part, detailed methodological explanation with formulae, worked calculations for (b), and specific Indian statistical system references for (c).
Key points expected
- Part (a): Identification of ARIMA model components (AR, I, MA), stationarity testing via ADF or KPSS, differencing procedures, ACF/PACF analysis for order identification, parameter estimation via maximum likelihood, diagnostic checking with Ljung-Box test, and forecasting with confidence intervals
- Part (b): Correct application of aggregative method (Laspeyres or Paasche formula with base year quantities as weights) and weighted relatives method (price relatives multiplied by base year expenditure weights), proper identification of missing data items from 'above data' reference, and meaningful economic interpretation of cost of living changes
- Part (c): Explanation of price quotation system (selection of representative items, specification of quality, choice of markets, timing of collection), role of NSSO and CSO in price data collection, and detailed coverage of DGCI&S publications (Monthly Statistics of Foreign Trade, Annual Report, commodity-wise/country-wise trade data, ITC-HS classification)
- Integration of Indian context: citing RBI's use of ARIMA for monetary policy forecasting, CPI-AL/RL/CPI-U/CPI-IW construction by Labour Bureau, and Ministry of Commerce's trade statistics dissemination
- Critical commentary in (b) on limitations of index numbers (substitution bias, quality changes, new goods) and in (c) on challenges in price quotation representativeness and trade data timeliness
- Correct mathematical notation: ∇^d for differencing, φ(B) and θ(B) operators, p/d/q orders, and index number formulae with proper subscripts
Evaluation rubric
| Dimension | Weight | Max marks | Excellent | Average | Poor |
|---|---|---|---|---|---|
| Setup correctness | 20% | 10 | For (a) correctly defines stationarity, explains identification-estimation-diagnostic-forecasting stages with proper notation; for (b) identifies correct base/current year, quantities, and prices from data; for (c) accurately describes price quotation criteria and names correct DGCI&S publications | Basic stage identification in (a) with minor notation errors; (b) has some data misidentification but correct formula structure; (c) mentions price collection without systematic criteria and lists only generic trade publications | Confuses ARIMA with ARMA or lacks differencing explanation; (b) uses wrong base year or swaps price/quantity; (c) conflates price quotations with general price statistics, omits key publications |
| Method choice | 20% | 10 | (a) Explains ACF/PACF patterns for AR vs MA identification and model selection criteria (AIC/BIC); (b) correctly selects Laspeyres aggregative and weighted relatives formulae with justification; (c) distinguishes between WPI/CPI price quotations and explains ITC-HS classification for trade | States methods without justification; (b) applies formulae correctly but doesn't explain why these specific methods; (c) describes publications without explaining their specific purposes | Wrong method selection (e.g., simple aggregative instead of weighted); (a) omits identification stage; (c) confuses DGCI&S with CSO publications |
| Computation accuracy | 20% | 10 | (b) Shows complete step-by-step calculations: Σp₁q₀/Σp₀q₀ for aggregative and ΣW(P₁/P₀)/ΣW for weighted relatives with correct arithmetic; (a) includes sample numerical illustration of differencing or parameter estimation if data provided | Correct formulae but arithmetic errors in final index; partial working shown; (a) describes computation without numbers | Major computational errors, wrong formula application, or missing calculations entirely; no numerical demonstration in (a) or (b) |
| Interpretation | 20% | 10 | (b) Meaningful comment on inflation magnitude, comparison between methods, and policy implications; (a) Explains diagnostic interpretation (residual analysis, overfitting); (c) Critical assessment of price quotation limitations (urban bias, quality changes) and trade data utility for balance of payments analysis | Generic comments without specific reference to calculated values; superficial critique without economic reasoning | No interpretation provided, or merely restates results without analysis; missing commentary on method differences in (b) |
| Final answer & units | 20% | 10 | Clear final index number with percentage interpretation for (b); (a) summarizes ARIMA model building as systematic iterative process; (c) provides comprehensive list of DGCI&S publications with their periodicity and coverage; all parts have precise concluding statements | Final answers present but poorly highlighted; some publications named without details; conclusion lacks synthesis | Missing final answers, no conclusion, or incomplete publication listing; (b) lacks index value or percentage change |
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