Stock Price Trends

Apple Inc (AAPL) 

Apple Inc. is an American multinational technology company that specializes in consumer electronics, computer software, and online services. Apple is the world's largest technology company by revenue (totalling $274.5 billion in 2020) and, since January 2021, the world's most valuable company. As of 2021, Apple is the world's fourth-largest PC vendor by unit sales, and fourth-largest smartphone manufacturer. It is one of the Big Five American information technology companies, along with Amazon, Google, Microsoft, and Facebook.

Stock Price Trends

Stock price trends estimated using linear regression.

Key facts

  • The primary trend is increasing.
  • The growth rate of the primary trend is 12.58% per annum.
  • AAPL price at the close of February 14, 2025 was $244.60 and was inside the primary price channel.
  • The secondary trend is increasing.
  • The growth rate of the secondary trend is 25.63% per annum.
  • AAPL price at the close of February 14, 2025 was inside the secondary price channel.

Linear Regression Model

Model equation:
Yi = α + β × Xi + εi

Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)

Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)

where:

i - observation number
Yi - natural logarithm of AAPL price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e


Primary Trend

Start date: August 13, 2020
End date: June 10, 2024

a = 4.7353

b = 0.0003

s = 0.0868

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.58%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.0868) – 1
= 41.53%

August 13, 2020 calculations

Top border of price channel:

Exp(Y124)
= Exp(a + b × X124 + 2 × s)
= Exp(a + b × 177 + 2 × s)
= Exp(4.7353 + 0.0003 × 177 + 2 × 0.0868)
= Exp(4.9664)
= $143.51

Bottom border of price channel:

Exp(Y124)
= Exp(a + b × X124 – 2 × s)
= Exp(a + b × 177 – 2 × s)
= Exp(4.7353 + 0.0003 × 177 – 2 × 0.0868)
= Exp(4.6191)
= $101.40

June 10, 2024 calculations

Top border of price channel:

Exp(Y1,085)
= Exp(a + b × X1,085 + 2 × s)
= Exp(a + b × 1,574 + 2 × s)
= Exp(4.7353 + 0.0003 × 1,574 + 2 × 0.0868)
= Exp(5.4198)
= $225.84

Bottom border of price channel:

Exp(Y1,085)
= Exp(a + b × X1,085 – 2 × s)
= Exp(a + b × 1,574 – 2 × s)
= Exp(4.7353 + 0.0003 × 1,574 – 2 × 0.0868)
= Exp(5.0725)
= $159.58

Description

  • The primary trend is increasing.
  • The growth rate of the primary trend is 12.58% per annum.
  • AAPL price at the close of February 14, 2025 was $244.60 and was inside the primary price channel.

Secondary Trend

Start date: September 23, 2022
End date: February 14, 2025

a = 4.3433

b = 0.0006

s = 0.0702

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 25.63%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.0702) – 1
= 32.40%

September 23, 2022 calculations

Top border of price channel:

Exp(Y656)
= Exp(a + b × X656 + 2 × s)
= Exp(a + b × 948 + 2 × s)
= Exp(4.3433 + 0.0006 × 948 + 2 × 0.0702)
= Exp(5.0762)
= $160.17

Bottom border of price channel:

Exp(Y656)
= Exp(a + b × X656 – 2 × s)
= Exp(a + b × 948 – 2 × s)
= Exp(4.3433 + 0.0006 × 948 – 2 × 0.0702)
= Exp(4.7956)
= $120.98

February 14, 2025 calculations

Top border of price channel:

Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.3433 + 0.0006 × 1,823 + 2 × 0.0702)
= Exp(5.6232)
= $276.78

Bottom border of price channel:

Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.3433 + 0.0006 × 1,823 – 2 × 0.0702)
= Exp(5.3426)
= $209.06

Description

  • The secondary trend is increasing.
  • The growth rate of the secondary trend is 25.63% per annum.
  • AAPL price at the close of February 14, 2025 was inside the secondary price channel.