Stock Price Trends

Amazon.com, Inc. (AMZN) 

Amazon.com, Inc. is an American multinational technology company focusing on e-commerce, cloud computing, online advertising, digital streaming, and artificial intelligence.

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 88.27% per annum.
  • AMZN price at the close of December 8, 2023 was $147.42 and was inside the primary price channel.
  • The secondary trend is increasing.
  • The growth rate of the secondary trend is 11.20% per annum.
  • AMZN price at the close of December 8, 2023 was higher than the top border of the secondary price channel by $0.42 (0.28%).

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 AMZN 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: November 18, 2022
End date: September 20, 2023

a = 1.9349

b = 0.0017

s = 0.0528

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0017) – 1
= 88.27%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.0528) – 1
= 23.51%

November 18, 2022 calculations

Top border of price channel:

Exp(Y994)
= Exp(a + b × X994 + 2 × s)
= Exp(a + b × 1,439 + 2 × s)
= Exp(1.9349 + 0.0017 × 1,439 + 2 × 0.0528)
= Exp(4.5348)
= $93.21

Bottom border of price channel:

Exp(Y994)
= Exp(a + b × X994 – 2 × s)
= Exp(a + b × 1,439 – 2 × s)
= Exp(1.9349 + 0.0017 × 1,439 – 2 × 0.0528)
= Exp(4.3237)
= $75.46

September 20, 2023 calculations

Top border of price channel:

Exp(Y1,202)
= Exp(a + b × X1,202 + 2 × s)
= Exp(a + b × 1,745 + 2 × s)
= Exp(1.9349 + 0.0017 × 1,745 + 2 × 0.0528)
= Exp(5.0653)
= $158.42

Bottom border of price channel:

Exp(Y1,202)
= Exp(a + b × X1,202 – 2 × s)
= Exp(a + b × 1,745 – 2 × s)
= Exp(1.9349 + 0.0017 × 1,745 – 2 × 0.0528)
= Exp(4.8541)
= $128.26

Secondary Trend

Start date: May 26, 2023
End date: November 6, 2023

a = 4.3786

b = 0.0003

s = 0.0407

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 11.20%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.0407) – 1
= 17.67%

May 26, 2023 calculations

Top border of price channel:

Exp(Y1,123)
= Exp(a + b × X1,123 + 2 × s)
= Exp(a + b × 1,628 + 2 × s)
= Exp(4.3786 + 0.0003 × 1,628 + 2 × 0.0407)
= Exp(4.9334)
= $138.86

Bottom border of price channel:

Exp(Y1,123)
= Exp(a + b × X1,123 – 2 × s)
= Exp(a + b × 1,628 – 2 × s)
= Exp(4.3786 + 0.0003 × 1,628 – 2 × 0.0407)
= Exp(4.7707)
= $118.01

November 6, 2023 calculations

Top border of price channel:

Exp(Y1,235)
= Exp(a + b × X1,235 + 2 × s)
= Exp(a + b × 1,792 + 2 × s)
= Exp(4.3786 + 0.0003 × 1,792 + 2 × 0.0407)
= Exp(4.9811)
= $145.64

Bottom border of price channel:

Exp(Y1,235)
= Exp(a + b × X1,235 – 2 × s)
= Exp(a + b × 1,792 – 2 × s)
= Exp(4.3786 + 0.0003 × 1,792 – 2 × 0.0407)
= Exp(4.8184)
= $123.77