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 66.53% per annum.
- ISRG price at the close of January 17, 2025 was $592.64 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 55.97% per annum.
- ISRG price at the close of January 17, 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 ISRG 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 17, 2023
End date: January 17, 2025
a = 3.8021
b = 0.0014
s = 0.0504
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 66.53%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0504) – 1
= 22.35%
August 17, 2023 calculations
Top border of price channel:
Exp(Y900)
= Exp(a + b × X900 + 2 × s)
= Exp(a + b × 1,304 + 2 × s)
= Exp(3.8021 + 0.0014 × 1,304 + 2 × 0.0504)
= Exp(5.7250)
= $306.42
Bottom border of price channel:
Exp(Y900)
= Exp(a + b × X900 – 2 × s)
= Exp(a + b × 1,304 – 2 × s)
= Exp(3.8021 + 0.0014 × 1,304 – 2 × 0.0504)
= Exp(5.5232)
= $250.44
January 17, 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(3.8021 + 0.0014 × 1,823 + 2 × 0.0504)
= Exp(6.4501)
= $632.77
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(3.8021 + 0.0014 × 1,823 – 2 × 0.0504)
= Exp(6.2484)
= $517.16
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 66.53% per annum.
- ISRG price at the close of January 17, 2025 was $592.64 and was inside the primary price channel.
Secondary Trend
Start date: January 10, 2024
End date: January 17, 2025
a = 4.1052
b = 0.0012
s = 0.0352
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 55.97%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0352) – 1
= 15.11%
January 10, 2024 calculations
Top border of price channel:
Exp(Y1,000)
= Exp(a + b × X1,000 + 2 × s)
= Exp(a + b × 1,450 + 2 × s)
= Exp(4.1052 + 0.0012 × 1,450 + 2 × 0.0352)
= Exp(5.9413)
= $380.41
Bottom border of price channel:
Exp(Y1,000)
= Exp(a + b × X1,000 – 2 × s)
= Exp(a + b × 1,450 – 2 × s)
= Exp(4.1052 + 0.0012 × 1,450 – 2 × 0.0352)
= Exp(5.8005)
= $330.47
January 17, 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(4.1052 + 0.0012 × 1,823 + 2 × 0.0352)
= Exp(6.3955)
= $599.12
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.1052 + 0.0012 × 1,823 – 2 × 0.0352)
= Exp(6.2547)
= $520.46
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 55.97% per annum.
- ISRG price at the close of January 17, 2025 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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