1. Core inflation model

Start with a simple model of the previous year's inflation representing the core inflation.

p* = 0.468 + 1.197p_t-1 - 0.088p_t-2 - 0.217p_t-3 + 0.048p_t-4

(A1)

To test the suitability of model by carrying out tests for autocorrelation, heteroskedasticity and mis-specification.

Testing for Error Autocorrelation from lags 1 to 5
Chi-squared(5) = 12.552 [0.0280] * and F-Form(5, 102) = 2.5748 [0.0309] *

Testing for Heteroscedastic errors
Chi-squared(8) = 18.501 [0.0178] * and F-Form(8, 98) = 2.4239 [0.0196] *

RESET test for adding Y2
RESET F( 1,106) = 0.34961 [0.5556]

p* = 0.450 + 1.229p_t-1 - 0.076p_t-2 - 0.191p_t-3 - 0.349p_t-4 + 0.486p_t-5 - 0.140p_t-6 + 0.031p_t-7 - 0.0448p_t-8

(A2)

Testing for Error Autocorrelation from lags 1 to 5
Chi-squared(5) = 29.3 [0.0000] ** and F-Form(5, 94) = 6.9993 [0.0000] **

Testing for Heteroscedastic errors
Chi-squarerd(16) = 23.569 [0.0994] and F-Form(16, 82) = 1.4306 [0.1482]

RESET test for adding Y2
RESET F( 1, 98) = 0.57972 [0.4483]

p* = 0.464 + 1.237p_t-1 - 0.293p_t-2

(A3)

Testing for Error Autocorrelation from lags 1 to 5
Chi-squared(5) = 15.106 [0.0099] ** and F-Form(5, 100) = 3.2523 [0.0092] **

Testing for Heteroscedastic errors
Chi-squared(4) = 12.077 [0.0168] * and F-Form(4, 100) = 3.1476 [0.0175] *

RESET test for adding Y2
RESET F( 1,104) = 0.11816 [0.7317]

p* = 0.426 + 1.234p_t-1 - 0.082p_t-2 - 0.206p_t-3 - 0.330p_t-4 + 0.498p_t-5 - 0.166p_t-6

(A4)

Testing for Error Autocorrelation from lags 1 to 5
Chi-squared(5) = 7.7057 [0.1732] and F-Form(5, 96) = 1.4752 [0.2051]

Testing for Heteroscedastic errors
Chi-squared(12) = 22.23 [0.0350] * and F-Form(12, 88) = 1.9007 [0.0449] *

RESET test for adding Y2
RESET F( 1,100) = 0.33303 [0.5652]

2. General Model

p_t = a + p_t* + S_i=0¹ b_ix_1t-i + S_i=0⁴ b_ix_2t-i + S_i=0¹² b_ix_3t-i

p_t = 0.042849 + 1.00011p_t* + 3.6829x_1t - 1.5933x_1t-1 - 0.00019950x_2t + 0.00039301x_2t-1 - 0.000041654x_2t-2 - 0.0000077147x_2t-3 + 0.0000012834x_2t-4 + 0.43954x_3t - 0.63818x_3t-1 - 1.0104x_3t-2 - 0.00397x_3t-3 + 1.0327x_3t-4 + 0.018703x_3t-5 + 0.75805x_3t-6 + 0.093992x_3t-7 - 1.2022x_3t-8 + 0.18240x_3t-9 + 0.52426x_3t-10 - 0.19963x_3t-11 + 0.059784x_3t-12

(A5)

Testing for Error Autocorrelation from lags 1 to 5
Chi-squared(5) = 7.9896 [0.1568] and F-Form(5, 77) = 1.2815 [0.2805]

Testing for Heteroscedastic errors
Chi-squared(29) = 28.923 [0.4691] and F-Form(29, 52) = 0.69077 [0.8573]

RESET test for adding Y2
RESET F( 1, 81) = 0.20154 [0.6547]

p_t = a + p_t* + S_i=0¹ b_ix_1t-i + S_i=0⁴ b_ix_2t-i + S_i=0⁸ b_ix_3t-i

p_t = 0.044409 + 0.99629p_t* + 0.92594x_1t + 0.31964x_1t-1 - 0.00018294x_2t + 0.00030178x_2t-1 - 0.000020155x_2t-2 + 0.000022311x_2t-3 - 0.0000022703x_2t-4 + 0.43243x_3t - 0.54418x_3t-1 - 0.93395x_3t-2 - 0.10061x_3t-3 + 1.0996x_3t-4 +0.10439x_3t-5 + 0.66770x_3t-6 +0.099075x3t-7 - 0.76516x_3t-8

(A6)

Testing for Error Autocorrelation from lags 1 to 5
Chi-squared(5) = 6.1857 [0.2886] and F-Form(5, 85) = 1.0328 [0.4037]

Testing for Heteroscedastic errors
Chi-squared(25) = 26.754 [0.3683] and F-Form(25, 64) = 0.84299 [0.6749]

RESET test for adding Y2
RESET F( 1, 89) =1.2673e-006 [0.9991]

p_t = a + p_t* + S_i=0¹ b_ix_1t-i + S_i=0⁴ b_ix^2t-i + S_i=0⁴ b_ix^3t-i

p_t = -0.096080 + 0.99517p_t* + 0.039207x_1t + 0.94839x_1t-1 - 0.000156x_2t + 0.000273x_2t-1 - 0.000022x_2t-2 + 0.00003254x_2t-3 - 0.0000266x_2t-4 + 0.38992x3t - 0.9017x_3t-1 -0.18939x_3t-2 - 0.18939x_3t-3 + 1.4065x_3t-4

(A7)

Testing for Error Autocorrelation from lags 1 to 5
Chi-squared(5) = 4.5131 [0.4781] and F-Form(5, 91) = 0.77866 [0.5676]

Testing for Heteroscedastic errors
Chi-squared(21) = 24.246 [0.2813] and F-Form(21, 74) = 0.99629 [0.4782]

RESET test for adding Y2
RESET F( 1, 95) = 0.037809 [0.8462]

pt = a + p_t* + b₁x_1t + b₂x_2t + b₃x3t

p_t = -0.0061309 + 1.0096p_t* + 0.48898x_1t + 0.0000899x_2t - 0.074345x_3t

(A8)

Testing for Error Autocorrelation from lags 1 to 5
Chi-squared(5) = 3.5088 [0.6221] and F-Form(5, 100) = 0.65898 [0.6554]

Testing for Heteroscedastic errors
Chi-squared(7) = 19.246 [0.0075] ** and F-Form(7, 97) = 2.9386 [0.0078] **

RESET test for adding Y2
RESET F( 1,104) = 0.29011 [0.5913]

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