Page 262 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Time Reversal Test

P × P
Time reversal test is satisfied if 01 10 = 1
∑ p q ∑ p q 92 91
01
0 0
P 10 = ∑ p q × ∑ p q = 199 × 202
11
1 0
202 199 92 91
P × P 10 = 91 × 92 × 199 × 202 = 1 = 1.
01
Hence time reversal test is satisfied.
Factor Reversal Test

Factor reversal test is satisfied if:
∑ p q
11
P × Q 01 = ∑ p q
01
00
∑ 10 ∑qp qp 92 199
11
Q 01 = ∑ 00 × ∑qp qp = 91 × 202
01
202 199 92 199 199
P × Q 01 = 91 × 92 × 91 × 202 = 91
01
Hence factor reversal test is satisfied.
Self-Assessment

1. Tick the correct Answer
(i) A good index number is one that satisfies
(a) Unit test (b) time reversal test
(c) factor reversal test (d) circular test
(e) all the test form.
(ii) Time reversal test is satisfied when
(a) P × P 10 = 0 (b) P × P 10 = 1
01
01
(c) P × 01 P 10 > 1 (d) P 01 × 10 <P 1

(iii) The circular test is satisfied when
(a) P × 12 P × 23 P 31 = 0 (b) P × 12 P × 23 P 13 = 1
(c) P × 12 P × 23 P = 1 (d) P × 12 P × 32 P = 0
31
31
(iv) The circular test is an extension of the
(a) unit test (b) time reversal test
(c) Factor reversal test (d) None of these
(v) Factor reversal test is satisfied when

∑ p q
11
(a) P × Q 01 = ∑ p q (b) ∑ pq
10
01
00
∑ p q
11
(c) P × Q 10 = ∑ p q (d) None of these
01
00
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