"Linear trend estimation is a statistical technique to aid interpretation of data."
The long-term direction of a time series.
Time Series Data: Understanding what time series data is and how it differs from cross-sectional data, including concepts such as trend, seasonality, cyclicity, etc.
Time Series Analysis: The process for analyzing and modeling time series data, typically involving methods such as decomposition, smoothing, forecasting, and regression.
Smoothing Techniques: The methods used to remove noise and reveal underlying trends in time series data, such as moving average, exponential smoothing, and trend removal filters.
Decomposition Methods: Techniques for separating a time series into its component parts, such as trend, seasonal effects, and random variations, including additive and multiplicative models.
Autocorrelation and Partial Autocorrelation: The measures of correlation between a time series and its lagged values, including autocorrelation and partial autocorrelation functions and their interpretation.
ARIMA Models: Autoregressive integrated moving average (ARIMA) models, which are commonly used for time series forecasting and involve functions such as autoregression, differencing, and moving average.
Seasonal ARIMA Models: ARIMA models that incorporate seasonality into the time series analysis, typically by including seasonal differencing, seasonal autoregression, and seasonal moving average.
Box-Jenkins Methodology: A popular approach for building time series models by using ARIMA models and a structured modeling process based on identification, estimation, and diagnostic testing.
Time Series Forecasting: The process of predicting future values of a time series by applying statistical models and other forecasting techniques, such as exponential smoothing, trend extrapolation, and regression analysis.
Applications of Trend Analysis: The fields of study and applications in which trend analysis is commonly used, including economics, finance, marketing, engineering, health care, and many others.
Linear Trend: A steady and gradual increase or decrease in value over time.
Seasonal Trend: Patterns in data that repeat themselves over a specific period, such as months or quarters.
Cyclical Trend: A pattern that occurs over a longer period, often years, and is influenced by economic, political, or societal factors.
Irregular Trend: Random fluctuations in data due to external factors that cannot be predicted or controlled.
Step Trend: A sudden and permanent shift in the data due to a specific event or change in the industry or market.
Autocorrelation Trend: A tendency for data to be correlated with its past values.
White Noise Trend: Random data with no discernible pattern or trend.
Trend with Seasonal Components: A combination of a linear trend and a seasonal trend, where the overall trend is impacted by seasonal patterns.
Trend with Cyclical Components: A combination of a linear trend and a cyclical trend, where the overall trend is impacted by longer-term cycles due to economic or social factors.
Trend with Irregular Components: A combination of a linear trend, seasonal trend, and irregular trend, where the overall trend is impacted by unpredictable external factors.
"Trend estimation can be used to make and justify statements about tendencies in the data, by relating the measurements to the times at which they occurred."
"This model can then be used to describe the behavior of the observed data, without explaining it."
"It may be useful to determine if measurements exhibit an increasing or decreasing trend which is statistically distinguished from random behavior."
"Some examples are determining the trend of the daily average temperatures at a given location from winter to summer, and determining the trend in a global temperature series over the last 100 years."
"Issues of homogeneity are important (for example, about whether the series is equally reliable throughout its length)." (Note: The paragraph is relatively short, so not all questions may have specific quotes to answer them directly. However, the provided quotes address the main aspects of the paragraph.)