i worked on the following tests and plots:
1.Standardized Residual Plot:

 This plot displays the standardized residuals of the model over time.
 Residuals are the differences between observed and predicted values.
 Ideally, residuals should fluctuate randomly around zero, without any discernible pattern.
 In our plot, we observed a fairly random scatter of residuals, although there are some instances of potential outliers.
 Histogram and Estimated Density Plot:
 The histogram bins the standardized residuals to show their distribution.
 An overlaid kernel density estimate (KDE) shows a smoothed version of this distribution.
 A standard normal distribution (N(0,1)) is plotted for comparison.
 A goodfitting model would have residuals that closely follow a normal distribution. The histogram should resemble the bell shape of the normal distribution curve.
 Normal QQ Plot:
 The quantilequantile plot compares the quantiles of the residuals with the quantiles of a normal distribution.
 If the residuals are normally distributed, the points should fall approximately along the red line.
 In the plot, the points largely follow the line, suggesting normality, but deviations at the ends may indicate heavier tails than the normal distribution.
 Correlogram (ACF Plot):
 The correlogram, or autocorrelation function plot, shows the correlation of the residuals with themselves at different lags.
 We look for correlations that are significantly different from zero at various lag intervals.
 In a wellfitted model, we expect that there will be no significant autocorrelation in the residuals. Here, most autocorrelations are within the confidence band, indicating no significant autocorrelation.