Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 63.79% per annum.
- AMAT price at the close of May 7, 2024 was $207.32 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 125.82% per annum.
- AMAT price at the close of May 7, 2024 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 AMAT 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 30, 2022
End date: May 7, 2024
a = 2.8338
b = 0.0014
s = 0.0752
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 63.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0752) – 1
= 35.09%
August 30, 2022 calculations
Top border of price channel:
Exp(Y835)
= Exp(a + b × X835 + 2 × s)
= Exp(a + b × 1,210 + 2 × s)
= Exp(2.8338 + 0.0014 × 1,210 + 2 × 0.0752)
= Exp(4.6199)
= $101.48
Bottom border of price channel:
Exp(Y835)
= Exp(a + b × X835 – 2 × s)
= Exp(a + b × 1,210 – 2 × s)
= Exp(2.8338 + 0.0014 × 1,210 – 2 × 0.0752)
= Exp(4.3191)
= $75.12
May 7, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.8338 + 0.0014 × 1,826 + 2 × 0.0752)
= Exp(5.4526)
= $233.36
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.8338 + 0.0014 × 1,826 – 2 × 0.0752)
= Exp(5.1518)
= $172.75
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 63.79% per annum.
- AMAT price at the close of May 7, 2024 was $207.32 and was inside the primary price channel.
Secondary Trend
Start date: September 21, 2023
End date: May 7, 2024
a = 1.3047
b = 0.0022
s = 0.0540
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0022) – 1
= 125.82%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0540) – 1
= 24.12%
September 21, 2023 calculations
Top border of price channel:
Exp(Y1,101)
= Exp(a + b × X1,101 + 2 × s)
= Exp(a + b × 1,597 + 2 × s)
= Exp(1.3047 + 0.0022 × 1,597 + 2 × 0.0540)
= Exp(4.9768)
= $145.00
Bottom border of price channel:
Exp(Y1,101)
= Exp(a + b × X1,101 – 2 × s)
= Exp(a + b × 1,597 – 2 × s)
= Exp(1.3047 + 0.0022 × 1,597 – 2 × 0.0540)
= Exp(4.7607)
= $116.83
May 7, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(1.3047 + 0.0022 × 1,826 + 2 × 0.0540)
= Exp(5.4878)
= $241.73
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.3047 + 0.0022 × 1,826 – 2 × 0.0540)
= Exp(5.2717)
= $194.75
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 125.82% per annum.
- AMAT price at the close of May 7, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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