Time Series Divider

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This excel file divides a time series whenever the linear trend of the time series changes. To achieve this, I used my own modified version of Quandt (1960) statistic. Since Quandt type dividing requires a regression model, I used a simple linear trend regression model as the underlying model.

Thin Plate Spline

The results of Thin Plate Spline Smoothing with 30 sample points

I have implemented Thin Plate Spline (TPS) smoothing for constructing initial Implied Volatility Surface estimate from limited data points that has different forward-moneyness grid points for each maturity. With this feature, I have tested the performance of TPS with a sample function.

Original function: sqrt( (x-0.5)^2 + (y-0,5)^2 )
domain: [0,1]x[0,1]
Construction of the input data: I generated 30 random points in the domain and calculated the theoretical function values of them.

After applying thin plate spline to 30 sample input points, we get the above approximated function values for each point in the grid on the domain [0,1]x[0,1].