Calculates the local/moving non-parametric regression (i.e., LOESS, LOWESS, etc.) forecast.

## Syntax

**NxLOCREG**(

**X**,

**Y**,

**P**,

**Kernel**,

**Alpha**,

**Optimize**,

**Target**,

**Return**)

- X
- is the x-component of the input data table (a one-dimensional array of cells (e.g., rows or columns)).
- Y
- is the y-component (i.e., function) of the input data table (a one-dimensional array of cells (e.g., rows or columns)).
- P
- is the polynomial order (0 = constant, 1= linear, 2=Quadratic, 3=Cubic, etc.), etc.). If missing, P = 0.
- Kernel
- is the weighting kernel function used with KNN-Regression method : 0(or missing)=Uniform, 1=Triangular, 2=Epanechnikov, 3=Quartic, 4=Triweight, 5=Tricube, 6=Gaussian, 7=Cosine, 8=Logistic, 9= Sigmoid, 10= Silverman.
Value Kernel 0 Uniform Kernel (default) 1 Triangular Kernel 2 Epanechnikov Kernel 3 Quartic Kernel 4 Triweight Kernel 5 Tricube Kernel 6 Gaussian Kernel 7 Cosine Kernel 8 Logistic Kernel 9 Sigmoid Kernel 10 Silverman Kernel - Alpha
- is the fraction of the total number (n) of data points that are used in each local fit (between 0 and 1). If missing or omitted, Alpha = 0.333.
- Optimize
- is a flag (True/False) for searching and using optimal bandwidth (i.e., fraction value or $\alpha$). If missing or omitted, optimize is assumed to be False.
- target
- is the desired x-value(s) to interpolate for (a single value or a one-dimensional array of cells (e.g., rows or columns)).
- Return
- is a number that determines the type of return value: 0=Forecast (default), 1=errors, 2=Smoothing parameter (bandwidth), 3=RMSE (CV). If missing or omitted, NxREG returns forecast/regression value(s).
Return Description 0 Forecast/Regression value(s) (default) 1 Forecast/Regression error(s) 2 Kernel Smoothing parameter (bandwidth) 3 RMSE (cross-validation)

## Remarks

- Local regression is a non-parametric method combining multiple regression models in a k-nearest-neighbor-based meta-model.
- Local regression or local polynomial regression, also known as moving regression, is a generalization of moving average and polynomial regression.
- Its most common methods initially developed for scatterplot smoothing are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing).
- Outside econometrics, LOESS is known and commonly referred to as Savitzky–Golay filter. Savitzky–Golay filter was proposed 15 years before LOESS.
- $\alpha$ is called the smoothing parameter because it controls the flexibility of the LOESS regression function. Large values of ${\displaystyle \alpha }$ produce the smoothest functions that wiggle the least in response to fluctuations in the data. The smaller ${\displaystyle \alpha }$ is, the closer the regression function will conform to the data. Using too small a value of the smoothing parameter is not desirable, however, since the regression function will eventually start to capture the random error in the data.
- The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variable (X).
- Observations (i.e., rows) with missing values in X or Y are removed.
- NxLOCREG is related to NxKREG, but NxLOCREG uses the nearest K-NN points to calculate kernel bandwidth and conduct its local regression.
- The time series may include missing values (e.g., #N/A) at either end.
- The NxLOCREG() function is available starting with version 1.66 PARSON.

## Files Examples

## Related Links

## References

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