To assess the order of integration of the variables, the Augmented Dickey–Fuller (ADF) test was applied, and the outcomes are presented in Table 2. The findings indicate that ITA, GDP, and FDI exhibit non-stationarity at their levels but become stationary after first differencing, implying that these variables are integrated of order one [I(1)]. Conversely, the inflation variable is stationary at its level, signifying integration at order zero [I(0)]. These results confirmed the appropriateness of the ARDL model for further analysis, as none of the variables were found to be I(2), which would violate the assumptions of the ARDL approach.

The model of the study assumes that international tourist arrivals are influenced by macroeconomic indicators such as GDP, FDI, and inflation. Thus, the functional specification of the ARDL model is expressed as: LITA t = f ( LITA t − 1 , LGDP t , LGDP t − 1 , LGDP t − 2 , LFDI t , LI t , LI t − 1 , LI t − 2 )

This functional relationship implies that the current value of international tourist arrivals depends on its own lag, and the current and lagged values of the selected macroeconomic variables.

Model in Regression Form (Structural Equation)

The functional model can be translated into the following regression form: LITA t = β 0 + β 1 LITA t − 1 + β 2 LGDP t + β 3 LGDP t − 1 + β 4 LGDP t − 2 + β 5 LFDI t + β 6 LI t + β 7 LI t − 1 + β 8 LI t − 2 + ε t

Where: •

LITA = Log of International Tourist Arrivals

This regression model explains how each variable, along with its lagged values, contributes to the variation in international tourist arrivals over time.

Following the stationarity analysis, the optimal ARDL model was chosen based on the Akaike Information Criterion (AIC), which identified the ARDL(1,2,0,2) model specification as the best fit. This configuration implies that one lag was included for the dependent variable (LITA), two lags for LGDP and LI, and no lag for LFDI. This model captures both short-run dynamics and long-run relationships among the variables. Table 3, presents the ARDL (1,2,0,2) estimation output. Figure 1, presents the AIC values for the top 20 models out of a total of 500 estimated models. Among all the models, Model 448, specified as ARDL(1,2,0,2), was identified as the optimal model. This selection is based on its lowest AIC value, approximately -2.56, suggesting that it provides the most efficient balance between capturing the underlying data patterns and avoiding overfitting. The substantial difference in AIC values between Model 448 and other models further reinforces its superiority in explaining the variability in the dataset with minimal information loss.

The regression output from the ARDL (1,2,0,2) model shows a strong goodness-of-fit, (R² = 0.9704, adjusted R² = 0.9565), indicating that over 95% of the variation in international tourist arrivals could be explained by the included regressors. The Durbin-Watson statistic of 2.13 further confirmed the absence of autocorrelation, thereby reinforcing the robustness and reliability of the estimated model. Among the short-run coefficients, changes in GDP (LGDP and its lags) were found to be statistically significant, underscoring the strong influence of economic growth on international tourist arrivals in the short term. Conversely, the coefficients for FDI and inflation were statistically insignificant, suggesting their short-run effects on tourist arrivals are minimal in the present context.

The AR(1) component of the model is represented by the inclusion of the lagged dependent variable: LITA t = β 0 + β 1 LITA t − 1 + u t

This reflects the dependence of the current level of tourist arrivals on its immediate past value, capturing momentum in tourism behavior.

The DL(2) structure in the ARDL(1,2,0,2) model is reflected in the inclusion of current and lagged values of the independent variables: LITA t = α + δ 1 LGDP t + δ 2 LGDP t − 1 + δ 3 LGDP t − 2 + δ 4 LFDI t + δ 5 LI t + δ 6 LI t − 1 + δ 7 LI t − 2 + v t

This DL model allows the impact of independent variables to be spread over time, acknowledging that macroeconomic shocks do not affect tourism instantaneously.

To investigate the presence of a long-run equilibrium relationship among the variables, the ARDL bounds testing procedure was employed ( Table 5). The result of F-statistic (F = 8.67) confirmed the presence of a long run cointegrating relationship among LITA, LGDP, LFDI, and LI. Table 4, presents the result of ARDL long run form test. The findings imply that, although short-run fluctuations may occur, these indicators tend to move together in the long run, maintaining a stable equilibrium relationship.

The long-run coefficients revealed that GDP had a statistically significant and positive relationship with international tourist arrivals. Specifically, a 1% increase in GDP was associated with an approximate 1.68% increase in international tourist arrivals, with a p-value less than 0.01( Table 3). The results aligns with the existing literature findings, suggesting that higher GDP levels enhance a country’s ability to attract tourists by improving infrastructure, accessibility, and service quality ( Song & Li, 2008). In contrast, the long-run coefficients for LFDI and LI were statistically insignificant, indicating that, in the context of this study, foreign investment and inflationary trends do not have a substantial long-term effect on inbound tourism. The constant term was marginally significant, possibly indicating a base level of tourist arrivals independent of macroeconomic conditions.

Table 6 presents the results of the ECM estimation. The error correction coefficient was -0.5129 and is statistically significant (p < 0.05).This finding suggests that any short-term disequilibrium between the variables does not persist indefinitely but rather converges back toward the long-run equilibrium path at a relatively fast pace. Specifically, about 51% of the deviations from the equilibrium level are corrected within a single period, suggesting that the model has a strong self-adjusting tendency. Within the short-run dynamics, both the contemporaneous and lagged first differences of GDP (D(LGDP) and D(LGDP(–1))) were found to be statistically significant. In contrast, inflation and its lagged values remained insignificant, suggesting that their short-run impact on tourist arrivals is minimal.

Overall, the results from all steps of the ARDL analysis point toward GDP being the most influential macroeconomic factor driving international tourist arrivals in India. The significance of the error correction coefficient confirms the existence and stability of the long-run relationship, while FDI and inflation, though theoretically relevant, do not demonstrate statistically significant impacts within this empirical framework.

To examine the assumption of homoskedasticity in the residuals of the ARDL (1, 2, 0, 2) model, the Breusch–Pagan–Godfrey test was employed (F-statistic = 0.3458 p-value = 0.9349, and Chi-square statistics = 0.8822, p-value = 0.9351). The results indicate that the residuals exhibit homoscedasticity, thereby providing no evidence of heteroskedasticity within the sample. The outcome validates one of the key classical linear regression assumptions, reinforcing the reliability of the estimated standard errors and the strength of inference drawn from the ARDL model in modelling the macroeconomic determinants of international tourist arrivals in India.

To validate the assumption of residual independence, the Breusch–Godfrey LM test for serial correlation was performed. The results yielded an F-statistic of 1.387 (p = 0.2801) and a Chi-square statistic of 4.0579 (p = 0.1315), both of which are statistically insignificant at the 5% level. These findings indicate that the null hypothesis of no serial correlation in the residuals up to the second lag cannot be rejected. Thus, the model passes the serial correlation diagnostic, confirming that the residuals are not autocorrelated and are independently distributed. This enhances the reliability of the coefficient estimates and ensures the robustness of inference drawn from the ARDL model in the context of analysing macroeconomic determinants of international tourist arrivals in India.

The residuals-versus-variables diagnostic plots presented in Figure 2 provide an assessment of the adequacy of the ARDL model specification. The scatterplots illustrate the distribution of residuals against each explanatory variable and their respective lagged terms, with fitted trend lines superimposed to detect any systematic patterns. The residuals appear to be randomly dispersed around the zero line across most variables, indicating that the assumptions of linearity and homoscedasticity are broadly satisfied. Notably, the plots for lagged international tourist arrivals [LITA(-1)] and GDP (LGDP) display stronger linear patterns, suggesting their significant explanatory power in the model. By contrast, the residual distributions for FDI (LFDI) and lagged inflation terms [LI(-1), LI(-2)] reveal weaker or more scattered associations, reflecting a relatively limited direct impact of these variables. Importantly, the absence of pronounced curvature or heteroscedastic spread in the residuals reinforces the structural adequacy and reliability of the estimated ARDL model, lending further credibility to the subsequent long-run and short-run estimates.

To assess the assumption of normality of the residuals in the estimated ARDL (1,2,0,2) model, the Jarque–Bera (JB) test was conducted. The Jarque–Bera (JB) statistic (JB = 11.17, p = 0.0038), at the 5% significance level, shows that the null hypothesis of normally distributed residuals is rejected, thereby indicating evidence of non-normality in the error terms. Despite this, the deviation from normality is not severe and can be attributed to the relatively small sample size (n = 26). Moreover, as the model satisfies other diagnostic conditions such as stability (as confirmed by the CUSUM test) and no serial correlation, the impact of non-normal residuals on estimation and inference is likely minimal. Nevertheless, this observation should be acknowledged as a limitation when interpreting hypothesis testing results derived from the ARDL model.

To assess the structural stability of the estimated ARDL(1,2,0,2) model, the CUSUM test was conducted. Figure 3 presents the CUSUM plot, where the test statistic (blue line) consistently remains within the 5% significance boundaries (orange dashed lines) over the entire sample period from 1995 to 2022, thereby indicating the structural stability of the model, confirming the relationship between ITA and the macroeconomic indicators - GDP, FDI, and inflation remained stable during the observed period. The stability of the model further enhances the credibility and reliability of the long-run and short-run coefficients estimated through the ARDL framework. This robustness supports the use of the model for policy interpretation and forecasting within the scope of India’s inbound tourism dynamics.

To evaluate the adequacy of functional form of the ARDL(1,2,0,2) model, Ramsey RESET test was conducted. It included square of the fitted values as an additional regressor to detect potential specification errors. The results showed an F-statistic of 3.4271 with a p-value of 0.0827, which is not statistically important at the conventional 5% level but indicates marginal significance at the 10% level. However, the Likelihood Ratio (LR) test yielded a statistic of 5.0461 with a p-value of 0.0247, which is significant at the 5% threshold. This mixed outcome proposes some evidence of possible functional form misspecification , particularly from the LR perspective. While the RESET test does not identify the exact source of the misspecification, it signals that non-linear terms or omitted variables may be contributing to model inefficiency. However, model satisfies other key diagnostic checks such as the non-appearance of serial correlation, homoskedasticity, and structural stability results of the RESET test should be viewed as a prompt for further model refinement rather than a rejection of model validity.