1 Introduction
Definition 1.0.1. A time series is an ordered sequence of observations \(x_1, x_2, \dots , x_n\). The ordering is usually in time, but it may be in another dimension, such as distance along a line.
What makes a time series a subject of its own is that its observations are dependent: this month’s value is related to last month’s. In most of statistics observations are assumed independent, and their order does not matter; in a time series the order is the most important thing about the data. Time series arise in every field:
- Agriculture: annual crop production, livestock numbers, crop prices.
- Business and economics: annual sales of a product, commodity prices, price indices such as inflation, stock-exchange earnings, exchange rates.
- Engineering: electrical signals, voltage, sound.
- Geophysics: the height of ocean waves, seismic records.
- Meteorology: sea-surface temperature, rainfall, wind speed.
- Medicine: annual mortality rates, failure rates of a surgical procedure.
- Quality control: measurements monitoring a production process.
- Social sciences: birth rates, mortality rates, accident and crime rates.
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