Investor emotional biases and trading volume’s asymmetric response: A non-linear ARDL approach tested in S&P500 stock market

Figures & data

Table 1. Unit root tests results

	ADF	PP	KPSS
In level
Price	−0.4159	−0.9103	3.8342**
Sent	−7.6479**	−20.6407**	0.3776*
TV	0.1302	−1.1316	4.5920**
In difference
Price	−14.1230**	−42.0100**	0.1053
Sent	−12.1763**	−126.1170**	0.0372
TV	−13.2606**	−116.3118**	0.1403

Notes: ADF denotes Augmented Dickey-Fuller unit root tests, PP refers to Phillips-Perron unit root tests, KPSS denotes Kwiatkowski–Phillips–Schmidt–Shin tests. The lag length in all the tests has been selected according to Akaike Information Criteria (AIC).

* Rejection of the null hypothesis at 10% level of significance.

** Rejection of the null hypothesis at 1% level of significance.

Table 2. Bounds test for non-linear cointegration

F-statistics	95% lower bound	95% upper bound	Conclusion
10.3728	2.86	4.01	Cointegration

Table 3. Dynamic non-linear estimation of the SP equation

	Coefficient	t-statistics
Constant	−1.4945***	−6.1997
TV(−1)	0.0818***	6.3022
Price_P(−1)	0.02044	1.1024
Price_N(−1)	0.0769 ***	4.1734
Sent_P(−1)	−0.0251	−1.2014
Sent_N(−1)	0.0363*	1.7865
DTV(−1)	0.3795***	14.1857
DTV(−2)	0.2400***	8.7212
DTV(−3)	0.2404***	8.8466
DTV(−4)	0.1692***	6.6895
DPrice_N	0.7287**	3.0257
DPrice_P(−1)	1.5689***	5.1387
DPrice_N(−1)	2.4617***	9.2099
DPrice_N(−3)	0.7635**	3.0270
Long-run coefficient
	Coefficient	p-value (F-stat)
Price_P	0.2496**	0.0281
Price_N	0.9391***	0.0001
Sent_P	0.3074*	0.0526
Sent_N	0.4442*	0.0914
Diagnostic tests
R-2	0.2538
R-2_AJ	0.2468
DW	2.0433
J-B	272.2091***
SC(12)	0.6762
HET	0.1007
FF	0.9271

* Rejection of the null hypothesis at 10% significance level.

** Rejection of the null hypothesis at 5% significance level.

*** Rejection of the null hypothesis at 1% significance level

Figure 1. Cusum and Cusum of squares at the 5% significance level.

Table 4. Asymmetry tests

	Long term asymmetry		Short-term asymmetry
	WLR	p-value	WSR	p-value
Stock price	−0.6895	0.0009	−0.05646	0.0008
Investor sentiment indicator	0.1367	0.0000	0.0111	0.0000

Notes: This table reports the results of the long- and short-term symmetry tests for the effect of stock price and investor sentiment indicator on trading volume. W_LR denotes the Wald statistic for the long-run symmetry, which tests the null hypothesis of θ⁺ = θ⁻ for each explanatory variable in Equation (6). W_SR corresponds to the Wald statistic for the short-run asymmetry, which tests the null hypothesis that ${\mathit{\pi }}_i^{+}={\mathit{\pi }}_i^{-}$ for each explanatory variable in Equation (8). The numbers in brackets are the associated p-values.

Figure 2. Asymmetric cumulative dynamic multiplier impact of lagged returns and sentiment on trading volume.

Notes: Black line shows the positive impact of the independent variable on the dependent variable while the Black dotted line shows the negative impact. The Red line shows the asymmetry in short term. And finally, the dotted Red lines show the upper and the lower bounds of the asymmetry.