**5. Conclusion**

The water parameters from different sources in the Tehri District of Uttarakhand have shown the non-platykurtic curve. The analysis of most of the water parameter combinations has shown the Brownian time series behavior with each other. The irregular pattern in the WQI can be used for prediction purposes by deciding if its dynamic follows a chaotic, random, or deterministic structural pattern. Mostly all groundwater variables like turbidity, chloride, iron, nitrate, pH, calcium, magnesium, fluoride, TDS, alkalinity, hardness, sulfate, etc. are affected by each other. The pH of the sample datasets shows the Brownian time series behavior with fluoride (Fl) parameter; persistent behavior with Ca, Mg, Fe, and nitrate; and anti-persistent performance with turbidity, chloride, TDS, alkalinity, hardness, and sulfate. Turbidity, chloride, nitrate, fluoride, TDS, alkalinity, sulfate, and chloride have shown persistent behavior with each other. Fe has persistent behavior with pH, Ca, and Mg, and nitrate has persistent behavior with turbidity, chloride, fluoride, TDS, alkalinity, hardness, and sulfate. pH has persistent behavior with Ca, Mg, Fe, and nitrate. Turbidity, chloride, TDS, alkalinity, hardness, Mg, Fl, TDS, sulfate, and Ca show persistent behavior. Mg has persistent behavior with turbidity, chloride, nitrate, Ca, TDS, hardness, Fl, and sulfate. Fl has persistent behavior with turbidity, chloride, TDS, alkalinity, and sulfate. TDS has persistent behavior with alkalinity, nitrate, and chloride. Alkalinity has persistent behavior with nitrate only. Hardness has persistent behavior with turbidity, chloride, nitrate, pH, Ca, Fl, TDS, alkalinity, and sulfate. Sulfate has persistent behavior with turbidity, chloride, TDS, and alkalinity.

Turbidity and chloride have anti-persistent behavior with Fe, pH, Ca, Mg, and hardness parameters. Fe has anti-persistent behavior with chloride, TDS, alkalinity, and sulfate parameters. Nitrate has anti-persistent behavior with Ca, Mg, Fe, and pH parameters. pH has anti-persistent performance with different parameters, i.e., turbidity, chloride, TDS, alkalinity, hardness, and sulfate. Mg has anti-persistent behavior with Fe parameters only and Ca with Fe and pH parameters. Fl has antipersistent behavior with Fe, pH, Ca, and Mg parameters. TDS has anti-persistent behavior with Fe, Ca, Mg, and hardness parameters. Alkalinity has anti-persistent behavior with turbidity, Fe, pH, Ca, Mg, and hardness parameters. Hardness has anti-persistent behavior with Fe parameter only, and sulfate has anti-persistent behavior with hardness, Fe, PH, Ca, and Mg parameters.

The persistent behavior is observed among the various indices which reveal that the variations of the water quality parameters are under an acceptable range with each other. This study is focused on the utility of the Hurst exponent, fractal dimension as an analysis tool, and predictability indices (PI) along with regression and coefficient of correlation among the water quality time series data points. It is concluded that the fractal analysis is a better statistical and mathematical tool to calculate water quality indices. Fractal analysis among the various parameters suggested that the water samples are good for drinking and the health.
