ARDL model questions

[Robbert Henk]

Hello all,

Im currently using an ARDL model in order to estimate the relationship between the log (ln) return (p/pt-1) of Bitcoin's price and several independent variables among which:
- log return of other exchanges
- log of exchange trading volumes
- Sentiment (no transformation)

Before transformation, DF test identified non-stationary as well as stationary variables. Hence, I end up using the ARDL model.
Using ARDL and the transformed variables, I also estimated whether there is cointegration.

Result of ARDL EC regression:

. ardl lnBp lnTrade lnNas lnSse lnHash Sent Gfsi, aic ec1 constant

ARDL(2,2,0,1,0,2,0) regression

Sample: 05may2011 - 28feb2018 Number of obs = 2492
R-squared = 0.4864
Adj R-squared = 0.4837
Log likelihood = 3943.9881 Root MSE = 0.0498

------------------------------------------------------------------------------
D.lnBp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ADJ |
lnBp |
L1. | -.9620244 .0273809 -35.13 0.000 -1.015716 -.9083326
-------------+----------------------------------------------------------------
LR |
lnTrade |
L1. | .0202743 .0040738 4.98 0.000 .0122859 .0282628
|
lnNas |
L1. | -.0243062 .1226179 -0.20 0.843 -.2647503 .2161378
|
lnSse |
L1. | .0033732 .1286853 0.03 0.979 -.2489687 .255715
|
lnHash |
L1. | .0002924 .0082516 0.04 0.972 -.0158883 .0164731
|
Sent |
L1. | .1018205 .0222358 4.58 0.000 .0582179 .1454231
|
Gfsi |
L1. | -.0063346 .0028494 -2.22 0.026 -.0119221 -.0007472
-------------+----------------------------------------------------------------
SR |
lnBp |
LD. | .0370142 .0200846 1.84 0.065 -.0023701 .0763986
|
lnTrade |
D1. | .0141216 .0017608 8.02 0.000 .0106687 .0175744
LD. | -.0039621 .0017755 -2.23 0.026 -.0074436 -.0004805
|
lnNas |
D1. | -.0233832 .117946 -0.20 0.843 -.2546661 .2078997
|
lnSse |
D1. | .1552682 .0883364 1.76 0.079 -.0179526 .3284889
|
lnHash |
D1. | .0002813 .0079384 0.04 0.972 -.0152852 .0158478
|
Sent |
D1. | .1450237 .019035 7.62 0.000 .1076976 .1823499
LD. | .0707588 .0190485 3.71 0.000 .0334061 .1081114
|
Gfsi |
D1. | -.0060941 .002748 -2.22 0.027 -.0114827 -.0007054
|
_cons | .0075057 .0013853 5.42 0.000 .0047892 .0102221
------------------------------------------------------------------------------
And the result for the bounds test:
. ardl,noctable btest

ARDL(2,2,0,1,0,2,0) regression

Sample: 05may2011 - 28feb2018 Number of obs = 2492
R-squared = 0.4864
Adj R-squared = 0.4837
Log likelihood = 3943.9881 Root MSE = 0.0498


note: estat btest has been superseded by estat ectest
as the prime procedure to test for a levels relationship.
(click to run)

Pesaran/Shin/Smith (2001) ARDL Bounds Test
H0: no levels relationship F = 178.642
t = -35.135

Critical Values (0.1-0.01), F-statistic, Case 3

| [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1]
| L_1 L_1 | L_05 L_05 | L_025 L_025 | L_01 L_01
------+----------------+----------------+----------------+---------------
k_6 | 2.12 3.23 | 2.45 3.61 | 2.75 3.99 | 3.15 4.43
accept if F < critical value for I(0) regressors
reject if F > critical value for I(1) regressors

Critical Values (0.1-0.01), t-statistic, Case 3

| [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1] | [I_0] [I_1]
| L_1 L_1 | L_05 L_05 | L_025 L_025 | L_01 L_01
------+----------------+----------------+----------------+---------------
k_6 | -2.57 -4.04 | -2.86 -4.38 | -3.13 -4.66 | -3.43 -4.99
accept if t > critical value for I(0) regressors
reject if t < critical value for I(1) regressors


As you can see, the F-statistic are very high and T-statistic low. Is that normal?

[Sebastian Kripfganz]

Given your large number of observations, that does not surprise me.

Please note that the btest option of the ardl command is outdated for some time already, as indicated by the note displayed in your output. Since version 1.0.0 of the ardl command, the bounds test is obtained with the postestimation command estat ectest. Please see the following Statalist topic for details:
ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

[Robbert Henk]

Hello Sebastian,

Thank you for your answer!