What Is an Autoregressive Integrated Moving Average (ARIMA)?

An autoregressive integrated moving average, or ARIMA, is a statistical analysis model that uses time series data to either better understand the data set or to predict future trends. 

A statistical model is autoregressive if it predicts future values based on past values. For example, an ARIMA model might seek to predict a stock’s future prices based on its past performance or forecast a company’s earnings based on past periods.

Understanding Autoregressive Integrated Moving Average (ARIMA)

An autoregressive integrated moving average model is a form of regression analysis that gauges the strength of one dependent variable relative to other changing variables. The model’s goal is to predict future securities or financial market moves by examining the differences between values in the series instead of through actual values.

An ARIMA model can be understood by outlining each of its components as follows:

• Autoregression (AR): refers to a model that shows a changing variable that regresses on its own lagged, or prior, values.
• Integrated (I): represents the differencing of raw observations to allow the time series to become stationary (i.e., data values are replaced by the difference between the data values and the previous values).
• Moving average (MA):  incorporates the dependency between an observation and a residual error from a moving average model applied to lagged observations.

ARIMA Parameters

Each component in ARIMA functions as a parameter with a standard notation. For ARIMA models, a standard notation would be ARIMA with p, d, and q, where integer values substitute for the parameters to indicate the type of ARIMA model used. The parameters can be defined as:

• p: the number of lag observations in the model, also known as the lag order.
• d: the number of times the raw observations are differenced; also known as the degree of differencing.
• q: the size of the moving average window, also known as the order of the moving average.

For example, a linear regression model includes the number and type of terms. A value of zero (0), which can be used as a parameter, would mean that particular component should not be used in the model. This way, the ARIMA model can be constructed to perform the function of an ARMA model, or even simple AR, I, or MA models.

ARIMA and Stationary Data

In an autoregressive integrated moving average model, the data are differenced in order to make it stationary. A model that shows stationarity is one that shows there is constancy to the data over time. Most economic and market data show trends, so the purpose of differencing is to remove any trends or seasonal structures. 

Seasonality, or when data show regular and predictable patterns that repeat over a calendar year, could negatively affect the regression model. If a trend appears and stationarity is not evident, many of the computations throughout the process cannot be made and produce the intended results.

How to Build an ARIMA Model

To begin building an ARIMA model for an investment, you download as much of the price data as you can. Once you’ve identified the trends for the data, you identify the lowest order of differencing (d) by observing the autocorrelations. If the lag-1 autocorrelation is zero or negative, the series is already differenced. You may need to difference the series more if the lag-1 is higher than zero.

Next, determine the order of regression (p) and order of moving average (q) by comparing autocorrelations and partial autocorrelations. Once you have the information you need, you can choose the model you’ll use.

Pros and Cons of ARIMA

ARIMA models have strong points and are good at forecasting based on past circumstances, but there are more reasons to be cautious when using ARIMA. In stark contrast to investing disclaimers that state “past performance is not an indicator of future performance…,” ARIMA models assume that past values have some residual effect on current or future values and use data from the past to forecast future events.

The following table lists other ARIMA traits that demonstrate good and bad characteristics.

The Bottom Line

The ARIMA model is used as a forecasting tool to predict how something will act in the future based on past performance. It is used in technical analysis to predict an asset’s future performance.

ARIMA modeling is generally inadequate for long-term forecastings, such as more than six months ahead, because it uses past data and parameters that are influenced by human thinking. For this reason, it is best used with other technical analysis tools to get a clearer picture of an asset’s performance.

What Is Accrued Liability?

The term “accrued liability” refers to an expense incurred but not yet paid for by a business. These are costs for goods and services already delivered to a company for which it must pay in the future. A company can accrue liabilities for any number of obligations and are recorded on the company’s balance sheet. They are normally listed on the balance sheet as current liabilities and are adjusted at the end of an accounting period.

Understanding Accrued Liability

An accrued liability is a financial obligation that a company incurs during a given accounting period. Although the goods and services may already be delivered, the company has not yet paid for them in that period. They are also not recorded in the company’s general ledger. Although the cash flow has yet to occur, the company must still pay for the benefit received.

Accrued liabilities, which are also called accrued expenses, only exist when using an accrual method of accounting. The concept of an accrued liability relates to timing and the matching principle. Under accrual accounting, all expenses are to be recorded in financial statements in the period in which they are incurred, which may differ from the period in which they are paid.

The expenses are recorded in the same period when related revenues are reported to provide financial statement users with accurate information regarding the costs required to generate revenue.

The cash basis or cash method is an alternative way to record expenses. But it doesn’t accrue liabilities. Accrued liabilities are entered into the financial records during one period and are typically reversed in the next when paid. This allows for the actual expense to be recorded at the accurate dollar amount when payment is made in full.

Types of Accrued Liabilities

There are two types of accrued liabilities that companies must account for, including routine and recurring. We’ve listed some of the most important details about each below.

Routine Accrued Liabilities

This kind of accrued liability is also referred to as a recurring liability. As such, these expenses normally occur as part of a company’s day-to-day operations. For instance, accrued interest payable to a creditor for a financial obligation, such as a loan, is considered a routine or recurring liability. The company may be charged interest but won’t pay for it until the next accounting period.

Non-Routine Accrued Liabilities

Non-routine accrued liabilities are expenses that don’t occur regularly. This is why they’re also called infrequent accrued liabilities. They aren’t part of a company’s normal operating activities. A non-routine liability may, therefore, be an unexpected expense that a company may be billed for but won’t have to pay until the next accounting period.

Journal Entry for an Accrued Liability

Accounting for an accrued liability requires a journal entry. An accountant usually marks a debit and a credit to their expense accounts and accrued liability accounts respectively.

This is then reversed when the next accounting period begins and the payment is made. The accounting department debits the accrued liability account and credits the expense account, which reverses out the original transaction.

When Do Accrued Liabilities Occur?

Accrued liabilities arise for a number of reasons or when events occur during the normal course of business. For instance:

• A company that purchases goods or services on a deferred payment plan accrues liabilities because the obligation to pay in the future exists.
• Employees may perform work for which they haven’t received wages.
• Interest on loans may be accrued if interest fees were incurred since the previous loan payment.
• Taxes owed to governments may be accrued because they are not due until the next tax reporting period.

At the end of a calendar year, employee salaries and benefits must be recorded in the appropriate year, regardless of when the pay period ends and when paychecks are distributed. For example, a two-week pay period may extend from December 25 to January 7.

Although they aren’t distributed until January, there is still one full week of expenses for December. The salaries, benefits, and taxes incurred from Dec. 25 to Dec. 31 are deemed accrued liabilities. These expenses are debited to reflect an increase in the expenses. Meanwhile, various liabilities will be credited to report the increase in obligations at the end of the year.

Accrued Liability vs. Accounts Payable (AP)

Accrued liabilities and accounts payable (AP) are both types of liabilities that companies need to pay. But there is a difference between the two. Accrued liabilities are for expenses that have not yet been billed, either because they are a regular expense that doesn’t require a bill (i.e., payroll) or because the company hasn’t yet received a bill from the vendor (i.e., a utility bill).

As such, accounts payable (or payables) are generally short-term obligations and must be paid within a certain amount of time. Creditors send invoices or bills, which are documented by the receiving company’s AP department. The department then issues the payment for the total amount by the due date. Paying off these expenses during the specified time helps companies avoid default.

Examples of Accrued Liability

As noted above, companies can accrue liabilities for many different reasons. As such, there are many different kinds of expenses that fall under this category. The following are some of the most common examples:

• Wage expenses: This is for work already performed by employees. The work is paid for in the next accounting period. This is common with employers who pay their employees bi-weekly, because a pay period may extend into the following accounting month or year.
• Goods and services: Some companies place orders and receive goods and services from their suppliers without paying for them immediately. As an accrued expense, the receiving company pays for these goods and services at a later date.
• Interest: A company may have an outstanding loan for which the interest isn’t yet due. The lender may require this expense.

What Is Adverse Possession?

The term “adverse possession” refers to a legal principle that grants title to someone who resides on or is in possession of another person’s land. The property’s title is granted to the possessor as long as certain conditions are met including whether they infringe on the rights of the actual owner and whether they are in continuous possession of the property. Adverse possession is sometimes called squatter’s rights, although squatter’s rights are a colloquial reference to the idea rather than a recorded law.

Understanding Adverse Possession

As mentioned above, adverse possession is a legal situation that occurs when one party is granted title to another person’s property by taking possession of it. This can happen intentionally or unintentionally with or without the property owner’s knowledge.

In cases of intentional adverse possession, a trespasser or squatter—someone who occupies another person’s land illegally—knowingly comes on to another person’s land to live on it and/or take it over. In other cases, adverse possession may be unintentional. For example, a homeowner may build a fence separating their yard without realizing they’ve crossed over and encroached on their neighbor’s property line. In either case, the adverse possessor—also referred to as the disseisor—can lay claim to that property. And if the claimant is successful in proving adverse possession, they are not required to pay the owner for the land.

Requirements to Prove Adverse Possession

The requirements to prove adverse possession tend to vary between jurisdictions. In many states, proof of payment for the taxes on a property and a deed is essentially required for the claimant to be successful. Each state has a time period during which the landowner of record can invalidate the claim at any time. For example, if the state threshold is 20 years and the landlord paints or pays for other maintenance on the house in question in the 19th year, then the claimant will have a difficult time proving adverse possession. That said, landowners are advised to remove the possibility of adverse possession as soon as possible by having signed agreements for any use of an owned property.

To successfully claim land under adverse possession, the claimant must demonstrate that his or her occupation of the land meets the following requirements:

• Continuous use: Under this condition, the adverse possessor must show they’ve been in continuous and uninterrupted possession of the property in question.
• Hostile and adverse occupation of the property: Although this doesn’t mean that the disseisor uses force to take the land, they must show there is no existing agreement or license from the landowner such as a written easement, lease, or rent agreement.
• Open and notorious possession: The person seeking adverse possession must occupy a property in a manner that is open, notorious, and obvious. The true owner is not required, however, to be aware of the occupation.
• Actual possession: The possessor must actively possess the property for the state’s predetermined statutory period, which may vary from three to 30 years. Possession may involve maintaining the land and—depending on state law—paying taxes.
• Exclusive use: The property is used solely by the disseisor, excluding any others from using it as well.

How to Prevent Adverse Possession

If you are a landowner, you can prevent a trespasser from gaining property ownership by taking some easy measures:

• Identify and mark your property boundaries. Inspect your land regularly for signs of trespassers. You may want to use “no trespassing” signs and block entrances with gates. Although many states will not find a “no trespassing” sign sufficient to prevent an adverse possession claim, it’s a good way to deter trespassers.
• Offer to rent the property to the trespasser. With a proper rental agreement in place, the trespasser cannot claim adverse possession.
• Grant written permission to someone to use your land, and make sure you get their written acknowledgment.
• Act fast. In the event of trespassing, you must act before the trespasser has been on your land for the period of time detailed by your jurisdiction, in order to make a successful case.

Adverse Possession vs. Homesteading

Adverse possession is similar to homesteading in practice. In homesteading, government-owned land or property with no clear owner on record is granted to new owners provided they are using and improving it. If a homesteader doesn’t use the land, they can lose it. Adverse possession can operate in a similar manner by freeing up land with an unclear title for productive use.

Of course, adverse possession can also be abused in ways homesteading cannot. If there is an informal easement between two farms where one farmer’s fence has an acre of the neighbors’ land in it, for example, the farmer using it can claim adverse possession to essentially bite off that chunk of land if there is no written easement agreement.

What Is Average Propensity to Consume?

Average propensity to consume (APC) measures the percentage of income that is spent rather than saved. This may be calculated by a single individual who wants to know where the money is going or by an economist who wants to track the spending and saving habits of an entire nation.

In either case, the propensity to consume can be determined by dividing average household consumption, or spending, by average household income, or earnings.

Understanding Average Propensity to Consume

From the broader economic view, a high average propensity to consume is generally good for the economy. When the average propensity to consume is high, consumers are saving less and spending more on goods or services. This increased demand drives economic growth, business expansion, and broad employment.

Low-income households are often seen as having a higher average propensity to consume than high-income households. Low-income households may be forced to spend their entire income on necessities with minimal disposable income remaining to save. Alternatively, high-income households with higher cash flow after their necessities are met typically have a relatively lower average propensity to consume.

Economists often gauge economy forecasts on actions by the middle-income households. The spending and savings patterns of this demographic often indicate a degree of confidence or pessimism about their own personal financial situations and the economy as a whole.

Propensity to Consume vs. Propensity to Save

The sum of the average propensity to consume and the average propensity to save is always equivalent to one. A household or a nation must either spend or save all of its income.

The inverse of the average propensity to consume is the average propensity to save (APS). That figure is simply the total of income minus spending. The result is known as the savings ratio.

Notably, the savings ratio is normally based on its percentage of disposable income, or after-tax income. An individual determining personal propensities to consume and save should probably use the disposable income figure as well for a more realistic measure.

Example of Average Propensity to Consume

Assume a nation’s economy has a gross domestic product (GDP) equivalent to its disposable income of $500 billion for the previous year. The total savings of the economy was $300 billion, and the rest was spent on goods and services.

The nation’s APS is calculated to be 0.60, or $300 billion/$500 billion. This indicates the economy allocated 60% of its disposable income to savings. The average propensity to consume is calculated to be 0.40, or (1 – 0.60). Therefore, the nation spent 40% of its GDP on goods and services.

APS can include saving for retirement, a home purchase, and other long-term investments. As such, it can be a proxy for national financial health.

Special Considerations

The marginal propensity to consume (MPC) is a related concept. It measures the change in the average propensity to consume.

Assume that the nation in the previous example increased its GDP to $700 billion and its consumption of goods and services rose to $375 billion. The economy’s average propensity to consume increased to 53.57%.

The nation’s consumption increased from $200 billion to $375 billion. Alternatively, the nation’s GDP increased from $500 billion to $700 billion. The nation’s marginal propensity to consume is 87.5% ($375 billion – $200 billion) / ($700 billion – $500 billion). The marginal propensity measures the directional trend of how an entity is utilizing its money. In this case, 87.5% of new growth was further consumed.