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The changes look messy and have no pattern. They can be caused by unexpected events like disasters or sudden news.

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Cyclical means changes that happen over a longer time, like ups and downs in the economy (business cycles). It's different from seasonal patterns because it doesn’t happen at the same time every year. It might take a few years to go up and down.

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This chart shows the changes in the number of active pulmonary TB cases reported monthly in a certain area from 2004 to 2013. The figure reflects the irregular fluctuations remaining after removing the trend and seasonality in the tuberculosis incidence data.

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The irregular or random component captures unpredictable, non-recurring fluctuations in a time series after removing trend, seasonal, and cyclical effects.

Key Characteristics:

Unpredictable Variations: These are erratic changes that do not follow a pattern and are often due to unforeseen events.

Short-Term Effects: Typically, these fluctuations are short-lived and do not persist over time.

Examples: Sudden market crashes, natural disasters, or unexpected political events impacting economic indicators.

Graph Description: The graph above illustrates a time series with irregular fluctuations, showing random spikes and drops without any discernible pattern, emphasizing the unpredictable nature of this component.

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In the graph, the number of active pulmonary TB cases exhibits regular, annually recurring fluctuations, representing a typical seasonal pattern that may reflect the influence of climatic changes and other factors.

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This graph shows the number of lynx captured in Canada each year between 1820 and 1935. The graph shows obvious cyclical fluctuations: the number of lynx rises and falls sharply every few years, but the length and amplitude of each cycle are not fixed. This phenomenon reflects the predator-prey relationship in the ecosystem and is a typical cyclical time series component, which is different from seasonal fluctuations with fixed periods.

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An irregular time-series is a collection of data points collected at uneven or random times, not at regular intervals.

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Cyclical variation refers to wave-like patterns in time series data that occur over long periods and are not of fixed frequency. These patterns are usually influenced by economic or business conditions (e.g., expansion and recession).

Key Traits: Fluctuations that rise and fall but are not seasonal. Unlike seasonal variations, cyclical cycles are not fixed in length or timing.

Example: Long-term changes in GDP due to economic cycles.

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This graph shows the seasonal variation of average daily energy consumption (kWh/day) by month over a 10-year period (2010–2019)

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Cyclic refers to the fluctuation occur over longer period and it does not have fixed period.

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Unpredictable, random variations caused by unusual or unexpected events.

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Example, after Trump announce the tariffs the stock go down

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Irregular

- Unpredictable variations remaining after trend, seasonal, and cyclical effects are removed.

-Example: A sudden drop in sales due to a natural disaster, such as flooding that forces store closures.

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Fluctuations with no fixed period, often linked to economic or business cycles.

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It is an unpredictable factor, the data that cannot be attributed to trend, seasonality, or cycles.

For example, sudden market crashes and natural disasters

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Cyclical (C)

-Fluctuations over longer, variable periods, usually linked to economic cycles

-It can go up and down like seasonal patterns, but follows the overall trend and depends on the broader economic environment.

-Example: During a recession, sales may decline for a few years, during an economic boom, sales may gradually rise.

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Cyclic time series data exhibits recurring patterns or fluctuations that are not tied to fixed calendar intervals. These intervals are longer than seasonal variations.

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Seasonal component recur regularly (e.g. monthly or yearly)

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This chart shows the time series trend of the U.S. federal funds effective rate from 1955 to 2025, reflecting the long-term changes in interest rates in different economic cycles.

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The graph show seasonality across regions where the sales peak on May.

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This graph shows a steady upward trend over time. Although there are some small fluctuations in the middle, the overall direction is continuously increasing.

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Random variations caused by unpredictable events. For example, a sudden drop in airline bookings due to a natural disaster.

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Cyclical patterns are like the way people approach fitness over time. At first, there’s full commitment — hitting the gym regularly, eating clean, staying motivated. Then, without warning, the energy fades, routines break, and workouts get skipped. Eventually, the motivation returns and the cycle starts again. These ups and downs don’t follow a fixed schedule like the seasons, but they always seem to come back eventually. That’s what makes them cyclical — not predictable in timing, but likely to happen over and over again.

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No data pattern can determine the trend, like the eruption of Mount Fuji, which has over 100 years of data, but we still don’t know when the next eruption will occur.

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Cyclical patterns occur when there are fluctuations that are not of a fixed frequency. These are often observed in longer data sets and can be thought of as longer-term oscillations, differing from seasonality by not having a fixed period.

Example:

Stock market cycles or real estate price cycles over many years.

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Seasonal: It’s a season pattern. I would say seasonal has a consistent pattern over the years. like it’s the same pattern over and over again.

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Cyclical patterns shows over long periods like year.

Example, the GDP growth on the Malaysia plantation sector.

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Seasonal is refers to the repeating patterns at regular intervals caused by weather, holidays. The graph shows the seasonal weather and its degree of temperature.

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Seasonality represents patterns that repeat at regular intervals due to calendar or environmental influences (e.g., months, quarters).
Example: Retail sales peaking every December due to holiday shopping.

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The plot shows an overall trend of increasing marriages from 2017 to 2019, a sharp irregular drop in 2020 due to the pandemic, and a recovery upward in 2021 and 2022.

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It is a cyclical pattern and does not have a fixed period.

For example, economic expansions

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The pattern of sequence can be daily, monthly, quarterly, or yearly. For instance, daily data like temperature can be represented in a daily pattern. Similarly, monthly data like restaurant sales during paydays can be represented in a monthly pattern.

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Explanation:

This graph shows random, unpredictable fluctuations. Irregular components are caused by unexpected events such as natural disasters or global crises.

Example:

A sudden drop in air travel during COVID-19 is an irregular pattern.

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Explanation:

The graph illustrates waves over a longer period without fixed intervals. Cyclical components reflect economic or business cycles.

Example:

The housing market rising and falling every few years due to economic conditions is cyclical behavior.

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Regular, repeating patterns within fixed periods (every year, month, week).

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Seasonal time series data is recurring patterns at regular interval. Can be caused by calender events or economic conditions.

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It has no pattern, it's just random.

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Long-term fluctuations that are not of fixed length, often linked to economic or business cycles.

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Seasonal (S)

-Regular, repeating patterns that occur at fixed intervals (daily, monthly, and yearly).
-Sales spike every January due to holiday shopping such as Chinese New Year.

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Random, unpredictable variations that do not follow a pattern.

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The results are tracked for seasonal period. The periodic, recurring fluctuations within the data that occur at regular intervals. The sample shows the fluctuations in pattern of domestic airline passengers over a short period of time and usually during the summer (mid-term, June ) the number of passengers are high and it is the same patter over few years.

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The trend component shows a consistent upward pattern over time, representing long-term developments (e.g., population growth, inflation).

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A trend shows the long-term progression of the time series data — either upward, downward, or flat.

Graph Example: A steadily increasing sales figure over several years.

Explanation: Trends reflect persistent, long-term growth or decline, unaffected by short-term fluctuations. For instance, global temperature rise over decades.

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Trend refers to the long-term movement throughout time. It can be increasing or decrease over time. The graph shows an upward trend of number of sales over the year.

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A pattern that repeats at regular intervals (daily, monthly, yearly).

Example:

Retail sales spike during holidays (e.g., Black Friday or Christmas).

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Long-term overall movement in the data (upward, downward, or flat).

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Repeating patterns or cycles of behavior over a fixed period (For example: monthly or quarterly)

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A long-term increase or decrease in the data. It does not repeat in a regular pattern.

Example:

Global Average Temperature

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Trend is the overall long term pattern of the data either going up or down.

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Explanation:

This graph displays repeating patterns that occur at regular intervals. Seasonality is often driven by time of year, weather, holidays, etc.

Example:

Ice cream sales peak in summer and drop in winter every year — this is a seasonal pattern.

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The graph depicts an upward trend of annual sales over time.

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Explanation:

This graph shows a long-term upward trend. Trend represents the overall direction in which data moves over time, either increasing, decreasing, or stable.

Example:

An example is the increasing number of internet users over the past decade.

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Periodic fluctuation at regular intervals, yearly, monthly or weekly.

Example, graph of ice cream sales peaking in summer and dropping in winter.

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Short-term fluctuations repeat year after year. Example school holiday , Raya , raining season

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It is the long-term movement

For example, the rise in global temperatures over the decades, the sales of housing prices over the decades

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Regular, repeating patterns at fixed interval. For example, monthly sales peaking every December due to holidays.

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Long-term, underlying movement or direction of the data over time. It can be upward or downward trend, indicating an increase or decrease in the data values.

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The long-term progression or direction of the data over time.

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It also changes periodically, but the time of each cycle is not the same

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Trend (T)

-The long-term movement or direction in the data.

-Indicates whether values are increasing, decreasing, or stable over time.

-For example: A retail store’s total sales steadily increase every year as the business expands.

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It is usually the long-term direction of a time-series data. The trend is usually upward or downward on the movement of data. The sample shown is the downward trend of the US treasury bill contract over a period of 100 days.

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Shows the general direction in which data is moving over time, ignoring short-term fluctuations.

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This time series plot of COVID-19 deaths in Malaysia over the past 6 months primarily shows a trend component.

The overall direction of deaths is downward from May to early July, then upward from July to September, and finally downward again towards October.

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Periodic changes, with the same changes at the same intervals

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It is a predictable, repeating pattern.

For example, the new year season, the hari raya season

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The drawn line has an upward or downward trend

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Long-term increase or decrease. Example house price

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The long-term direction of the data. For example, the steady increase in average global temperatures over decades.