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 integer value K (i.e. number of data-points). If missing or omitted, optimize is assumed 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 (badwidth) |

3 | RMSE (cross-validation) |

## Remarks

- Local regression is a non-parametric regression methods that combine 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 very releated to NxKREG, but NxLOCRTEG uses 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

## References

- Pagan, A.; Ullah, A. (1999). Nonparametric Econometrics. Cambridge University Press. ISBN 0-521-35564-8.
- Simonoff, Jeffrey S. (1996). Smoothing Methods in Statistics. Springer. ISBN 0-387-94716-7.
- Li, Qi; Racine, Jeffrey S. (2007). Nonparametric Econometrics: Theory and Practice. Princeton University Press. ISBN 0-691-12161-3.
- Henderson, Daniel J.; Parmeter, Christopher F. (2015). Applied Nonparametric Econometrics. Cambridge University Press. ISBN 978-1-107-01025-3.

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