# Nonparametric Method of Least Squares: Accounting for Seasonality

## Abstract

We consider the problem of restoring a nonparametric dependence described by the sum of linear trend and seasonal component, i.e., a periodic function with the known period. We obtain the asymptotic distribution of the parameter estimates and the trend component. We find the mathematical expectation of the residual sum of squares. We also develop the methods of estimation of the seasonal component and construction of the interval forecast.

- Authors:

- Bauman Moscow State Technical University and Moscow Physics-Technical Institute (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771595

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 228; Journal Issue: 5; Conference: International seminar on stability problems for stochastic models, Zakopane (Poland), 31 May - 5 Jun 2009; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; FUNCTIONS; LEAST SQUARE FIT; PERIODICITY

### Citation Formats

```
Orlov, A. I., E-mail: prof-orlov@mail.ru.
```*Nonparametric Method of Least Squares: Accounting for Seasonality*. United States: N. p., 2018.
Web. doi:10.1007/S10958-017-3639-2.

```
Orlov, A. I., E-mail: prof-orlov@mail.ru.
```*Nonparametric Method of Least Squares: Accounting for Seasonality*. United States. doi:10.1007/S10958-017-3639-2.

```
Orlov, A. I., E-mail: prof-orlov@mail.ru. Thu .
"Nonparametric Method of Least Squares: Accounting for Seasonality". United States. doi:10.1007/S10958-017-3639-2.
```

```
@article{osti_22771595,
```

title = {Nonparametric Method of Least Squares: Accounting for Seasonality},

author = {Orlov, A. I., E-mail: prof-orlov@mail.ru},

abstractNote = {We consider the problem of restoring a nonparametric dependence described by the sum of linear trend and seasonal component, i.e., a periodic function with the known period. We obtain the asymptotic distribution of the parameter estimates and the trend component. We find the mathematical expectation of the residual sum of squares. We also develop the methods of estimation of the seasonal component and construction of the interval forecast.},

doi = {10.1007/S10958-017-3639-2},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 228,

place = {United States},

year = {2018},

month = {2}

}

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